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Welcome to the mathematics research hub for papers categorised under MSC 2010 classifications as Integral Equations. Papers on this page are organised in collections from 45- through 45R, although not all collections may have papers published in that area at this time. Visit the MSC2010 database from MathScinet for a full list of codes.

Jump to the following areas

45-XX: Integral equations 45Axx: Linear integral equations 45Bxx: Fredholm integral equations 45Cxx: Eigenvalue problems 45Dxx: Volterra integral equations 45Exx: Singular integral equations 45Fxx: Systems of linear integral equations 45Gxx: Nonlinear integral equations 45Hxx: Miscellaneous special kernels 45Jxx: Integro-ordinary differential equations 45Kxx: Integro-partial differential equations 45Lxx: Theoretical approximation of solutions 45Mxx: Qualitative behavior 45Nxx: Abstract integral equations, integral equations in abstract spaces 45Pxx: Integral operators 45Qxx: Inverse problems 45Rxx: Random integral equations

Integral equations (45-XX)

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Linear integral equations (45Axx)

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Article
Asymptotic Behaviour of the Energy Integral of a Two-Parameter Homogenization Problem with Nonlinear Periodic Robin Boundary Conditions
Massimo Lanza de Cristoforis, Paolo Musolino
Proceedings of the Edinburgh Mathematical Society, Volume 62, Issue 4

Article
Wave propagation for a class of non-local dispersal non-cooperative systems
Fei-Ying Yang, Wan-Tong Li, Jia-Bing Wang
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 4

Article
Nonlocal problems in perforated domains
Marcone C. Pereira, Julio D. Rossi
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 1

Article
Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain
Wei Zhang, Jiang Yang, Jiwei Zhang, Qiang Du
Communications in Computational Physics, Volume 21, Issue 1

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Fredholm integral equations (45Bxx)

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Article
An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems
Meng Zhao, Wenjun Ying, John Lowengrub, Shuwang Li
Communications in Computational Physics, Volume 21, Issue 3

Article
CONVERGENCE IN RELAXATION SPECTRUM RECOVERY
R. J. LOY, F. R. DE HOOG, R. S. ANDERSSEN
Bulletin of the Australian Mathematical Society, Volume 95, Issue 1

Article
Level-crossing probabilities and first-passage times for linear processes
Gopal K. Basak, Kwok-Wah Remus Ho
Advances in Applied Probability, Volume 36, Issue 2

Article
The integral representation for a solution of the 2-d Dirichlet problem with boundary data on closed and open curves
P. A. Krutitskii
Mathematika, Volume 47, Issue 1-2

Article
Analysis of a two-queue model with Bernoulli schedules
Duan-Shin Lee
Journal of Applied Probability, Volume 34, Issue 1

Article
On certain methods of solving a class of integral equations of Fredholm type
H. M. Srivastava, R. K. Raina
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 52, Issue 1

Article
Uniform convergence of regularization methods for Fredholm equations of the first kind
C. W. Groetsch
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 39, Issue 2

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Eigenvalue problems (45Cxx)

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Article
Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials
ELENA CHERKAEV, MINWOO KIM, MIKYOUNG LIM
European Journal of Applied Mathematics, Volume 33, Issue 3

Article
On finite sections of the multiplicative Hilbert inequalities
Charif Abdallah Benyamine
Canadian Mathematical Bulletin, Volume 65, Issue 1

Article
Nonlocal problems in perforated domains
Marcone C. Pereira, Julio D. Rossi
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 1

Article
Fractional eigenvalue problems that approximate Steklov eigenvalue problems
Leandro M. Del Pezzo, Julio D. Rossi, Ariel M. Salort
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 148, Issue 3

Article
Limit theorems for some branching measure-valued processes
Bertrand Cloez
Advances in Applied Probability, Volume 49, Issue 2

Article
Computing the Ground and First Excited States of the Fractional Schrödinger Equation in an Infinite Potential Well
Siwei Duo, Yanzhi Zhang
Communications in Computational Physics, Volume 18, Issue 2

Article
Spectral analysis of integro-differential operators applied in linear antenna modelling
Dave J. Bekers, Stephanus J. L. van Eijndhoven
Proceedings of the Edinburgh Mathematical Society, Volume 55, Issue 2

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Volterra integral equations (45Dxx)

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Article
Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media
Jie Yao, Anne-Cécile Lesage, Fazle Hussain, Donald J. Kouri
Communications in Computational Physics, Volume 20, Issue 2

Article
SIMPLE JOINT INVERSION LOCALIZED FORMULAE FOR RELAXATION SPECTRUM RECOVERY
R. S. ANDERSSEN, A. R. DAVIES, F. R. de HOOG, R. J. LOY
The ANZIAM Journal, Volume 58, Issue 1

Article
Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels
Xiulian Shi, Yanping Chen
Advances in Applied Mathematics and Mechanics, Volume 8, Issue 4

Article
Piecewise Legendre spectral-collocation method for Volterra integro-differential equations
Zhendong Gu, Yanping Chen
LMS Journal of Computation and Mathematics, Volume 18, Issue 1

Article
A Note on M/G/1 Vacation Systems with Sojourn Time Limits
Tsuyoshi Katayama
Journal of Applied Probability, Volume 49, Issue 4

Article
Some Results for Vacation Systems with Sojourn Time Limits
Tsuyoshi Katayama
Journal of Applied Probability, Volume 48, Issue 3

Article
EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES
MURAT ADıVAR, YOUSSEF N. RAFFOUL
Bulletin of the Australian Mathematical Society, Volume 82, Issue 1

Article
AN INTEGRAL EQUATION FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF A REFLECTED BROWNIAN MOTION
VICTOR DE-LA-PEÑA, GERARDO HERNÁNDEZ-DEL-VALLE, CARLOS G. PACHECO-GONZÁLEZ
The ANZIAM Journal, Volume 50, Issue 4

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Singular integral equations (45Exx)

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Article
MIXED BOUNDARY VALUE PROBLEM IN MICROFLUIDICS: THE AVER’YANOV–BLUNT MODEL REVISITED
ANVAR KACIMOV, YURII OBNOSOV
The ANZIAM Journal, Volume 67

Article
Uniqueness and Hyers–Ulam’s stability for a fractional nonlinear partial integro-differential equation with variable coefficients and a mixed boundary condition
Chenkuan Li
Canadian Journal of Mathematics, Volume 77, Issue 4

Article
On a critical time-harmonic Maxwell equation in nonlocal media
Minbo Yang, Weiwei Ye, Shuijin Zhang
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, First View

Article
On Liouville theorems of a Hartree–Poisson system
Ling Li, Yutian Lei
Proceedings of the Edinburgh Mathematical Society, Volume 66, Issue 4

Article
EXISTENCE OF TRAVELLING WAVES IN THE FRACTIONAL BURGERS EQUATION
ADAM CHMAJ
Bulletin of the Australian Mathematical Society, Volume 97, Issue 1

Article
DYNAMIC MULTI-STRUCTURE IN MODELLING A TRANSITION FLEXURAL WAVE
Alexander B. Movchan, Michele Brun, Leonid I. Slepyan, Gian F. Giaccu
Mathematika, Volume 61, Issue 2

Article
Some characterizations of exponential or geometric distributions in a non-stationary record value model
Hans-Jürgen Witte
Journal of Applied Probability, Volume 30, Issue 2

Article
The saturation phenomena for Tikhonov regularization
C. W. Groetsch, J. T. King
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 35, Issue 2

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Systems of linear integral equations (45Fxx)

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Article
Wave propagation for a class of non-local dispersal non-cooperative systems
Fei-Ying Yang, Wan-Tong Li, Jia-Bing Wang
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 4

Article
PREDATOR–PREY MODEL WITH AGE STRUCTURE
J. PROMRAK, G. C. WAKE, C. RATTANAKUL
The ANZIAM Journal, Volume 59, Issue 2

Article
MEMBRANE-COUPLED GRAVITY WAVE SCATTERING BY A VERTICAL BARRIER WITH A GAP
S. R. MANAM, R. B. KALIGATLA
The ANZIAM Journal, Volume 55, Issue 3

Article
The spectra of weighted mean operators on bν0
B. E. Rhoades
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 52, Issue 2

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Nonlinear integral equations (45Gxx)

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Article
Travelling wave solutions and spreading speeds for a scalar age-structured equation with nonlocal diffusion
Arnaud Ducrot, Hao Kang
European Journal of Applied Mathematics, Volume 36, Issue 4

Article
SUMMABILITY AND ASYMPTOTICS OF POSITIVE SOLUTIONS OF AN EQUATION OF WOLFF TYPE
CHUNHONG LI, YUTIAN LEI
Bulletin of the Australian Mathematical Society, Volume 110, Issue 3

Article
On a critical time-harmonic Maxwell equation in nonlocal media
Minbo Yang, Weiwei Ye, Shuijin Zhang
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, First View

Article
On Liouville theorems of a Hartree–Poisson system
Ling Li, Yutian Lei
Proceedings of the Edinburgh Mathematical Society, Volume 66, Issue 4

Article
OPTIMAL STOPPING PROBLEMS WITH A RANDOM TIME HORIZON
ZHUOSHU WU
Bulletin of the Australian Mathematical Society, Volume 108, Issue 2

Article
Propagation of minima for nonlocal operators
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 154, Issue 4

Article
Hardy–Littlewood–Sobolev inequality and existence of the extremal functions with extended kernel
Zhao Liu
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 153, Issue 5

Article
Steady-state solutions of one-dimensional competition models in an unstirred chemostat via the fixed point index theory
Kunquan Lan, Wei Lin
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 151, Issue 1

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Miscellaneous special kernels (45Hxx)

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Article
Continuum limit for interacting systems on adaptive networks
Sebastian Throm
European Journal of Applied Mathematics, First View

Article
Discounted probability of exponential parisian ruin: Diffusion approximation
Xiaoqing Liang, Virginia R. Young
Journal of Applied Probability, Volume 59, Issue 1

Article
Mass-conserving solutions to the Smoluchowski coagulation equation with singular kernel
Prasanta Kumar Barik, Ankik Kumar Giri, Philippe Laurençot
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 4

Article
MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS
REZA ALLAHYARI, REZA ARAB, ALI SHOLE HAGHIGHI
Bulletin of the Australian Mathematical Society, Volume 94, Issue 3

Article
Piecewise Legendre spectral-collocation method for Volterra integro-differential equations
Zhendong Gu, Yanping Chen
LMS Journal of Computation and Mathematics, Volume 18, Issue 1

Article
Oscillations of solutions of general integrodifferential equations
A. H. Nasr
Mathematika, Volume 39, Issue 1

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Integro-ordinary differential equations (45Jxx)

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Article
Continuum limit for interacting systems on adaptive networks
Sebastian Throm
European Journal of Applied Mathematics, First View

Article
Discounted probability of exponential parisian ruin: Diffusion approximation
Xiaoqing Liang, Virginia R. Young
Journal of Applied Probability, Volume 59, Issue 1

Article
Mass-conserving solutions to the Smoluchowski coagulation equation with singular kernel
Prasanta Kumar Barik, Ankik Kumar Giri, Philippe Laurençot
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 4

Article
MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS
REZA ALLAHYARI, REZA ARAB, ALI SHOLE HAGHIGHI
Bulletin of the Australian Mathematical Society, Volume 94, Issue 3

Article
Piecewise Legendre spectral-collocation method for Volterra integro-differential equations
Zhendong Gu, Yanping Chen
LMS Journal of Computation and Mathematics, Volume 18, Issue 1

Article
Oscillations of solutions of general integrodifferential equations
A. H. Nasr
Mathematika, Volume 39, Issue 1

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Integro-partial differential equations (45Kxx)

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Theoretical approximation of solutions (45Lxx)

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Article
Numerical Optimization and Noise Analysis of High-Tip-Speed Wind Turbine
Long Wang, Guoping Chen, Tongguang Wang, Jiufa Cao
Advances in Applied Mathematics and Mechanics, Volume 9, Issue 6

Article
Numerical Solution of Stochastic Ito-Volterra Integral Equations using Haar Wavelets
Fakhrodin Mohammadi
Numerical Mathematics: Theory, Methods and Applications, Volume 9, Issue 3

Article
SIMPLE JOINT INVERSION LOCALIZED FORMULAE FOR RELAXATION SPECTRUM RECOVERY
R. S. ANDERSSEN, A. R. DAVIES, F. R. de HOOG, R. J. LOY
The ANZIAM Journal, Volume 58, Issue 1

Article
Uniform convergence of regularization methods for Fredholm equations of the first kind
C. W. Groetsch
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 39, Issue 2

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Qualitative behavior (45Mxx)

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Article
SUMMABILITY AND ASYMPTOTICS OF POSITIVE SOLUTIONS OF AN EQUATION OF WOLFF TYPE
CHUNHONG LI, YUTIAN LEI
Bulletin of the Australian Mathematical Society, Volume 110, Issue 3

Article
Propagation of minima for nonlocal operators
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 154, Issue 4

Article
Existence of positive solutions for a class of semipositone problem in whole ℝN
Claudianor O. Alves, Angelo R. F. de Holanda, Jefferson A. dos Santos
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 5

Article
A NOTE ON RADIAL SYMMETRY FOR AN INTEGRAL EQUATION OF WOLFF TYPE
YUN WANG, LIXIN TIAN
Bulletin of the Australian Mathematical Society, Volume 100, Issue 2

Article
Nonlocal problems in perforated domains
Marcone C. Pereira, Julio D. Rossi
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 150, Issue 1

Article
Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
Dmitri Finkelshtein, Pasha Tkachov
Advances in Applied Probability, Volume 50, Issue 2

Article
Integrable Properties of a Variant of the Discrete Hungry Toda Equations and Their Relationship to Eigenpairs of Band Matrices
Yusuke Nishiyama, Masato Shinjo, Koichi Kondo, Masashi Iwasaki
East Asian Journal on Applied Mathematics, Volume 7, Issue 4

Article
The lack of exponential stability for a class of second-order systems with memory
Valeria Danese, Filippo Dell'Oro
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 147, Issue 4

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Abstract integral equations, integral equations in abstract spaces (45Nxx)

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Article
The invariant subspaces of periodic Fourier multipliers with application to abstract evolution equations
Sebastian Król, Jarosław Sarnowski
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, First View

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Integral operators (45Pxx)

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Article
Absolute continuity of distributions of one-dimensional Lévy processes
Tongkeun Chang
Journal of Applied Probability, Volume 54, Issue 3

Article
ESSENTIAL COMMUTATIVITY OF SOME INTEGRAL AND COMPOSITION OPERATORS
ZE-HUA ZHOU, LIANG ZHANG, HONG-GANG ZENG
Bulletin of the Australian Mathematical Society, Volume 85, Issue 1

Article
Non-weak compactness of the integration map for vector measures
S. Okada, W. J. Ricker
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 54, Issue 3

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Inverse problems (45Qxx)

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Article
Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media
Jie Yao, Anne-Cécile Lesage, Fazle Hussain, Donald J. Kouri
Communications in Computational Physics, Volume 20, Issue 2

Article
Wicksell's Problem in Local Stereology
Ó. Thórisdóttir, M. Kiderlen
Advances in Applied Probability, Volume 45, Issue 4

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Random integral equations (45Rxx)

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MSC 2010: Integral equations

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Integral equations (45-XX)

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Linear integral equations (45Axx)

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Fredholm integral equations (45Bxx)

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Eigenvalue problems (45Cxx)

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Volterra integral equations (45Dxx)

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Singular integral equations (45Exx)

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Systems of linear integral equations (45Fxx)

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Nonlinear integral equations (45Gxx)

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Miscellaneous special kernels (45Hxx)

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Integro-ordinary differential equations (45Jxx)

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Integro-partial differential equations (45Kxx)

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Theoretical approximation of solutions (45Lxx)

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Qualitative behavior (45Mxx)

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Abstract integral equations, integral equations in abstract spaces (45Nxx)

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Integral operators (45Pxx)

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Inverse problems (45Qxx)

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Random integral equations (45Rxx)

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