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Variational Methods for Nonlocal Fractional Problems
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  • Cited by 10
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bartolo, Rossella and Molica Bisci, Giovanni 2017. Asymptotically linear fractional p-Laplacian equations. Annali di Matematica Pura ed Applicata (1923 -),

    dos Prazeres, Disson and Wang, Ying 2017. Symmetry results for positive solutions of mixed integro-differential equations. Journal of Mathematical Analysis and Applications, Vol. 438, Issue. 2, p. 909.

    Giacomoni, J. Mishra, Pawan Kumar and Sreenadh, K. 2017. Fractional Kirchhoff equation with critical exponential nonlinearity. Complex Variables and Elliptic Equations, Vol. 61, Issue. 9, p. 1241.

    Li, Qin and Yang, Zuodong 2017. Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in ℝN. Complex Variables and Elliptic Equations, Vol. 61, Issue. 7, p. 969.

    Qiu, Hong and Xiang, Mingqi 2017. Existence of solutions for fractional p-Laplacian problems via Leray-Schauder’s nonlinear alternative. Boundary Value Problems, Vol. 2016, Issue. 1,

    Torres Ledesma, César E. 2017. Symmetric ground state solution for a non-linear Schrödinger equation with non-local regional diffusion. Complex Variables and Elliptic Equations, Vol. 61, Issue. 10, p. 1375.

    Xiang, Mingqi Zhang, Binlin and Yang, Miaomiao 2017. A fractional Kirchhoff-type problem in ℝNwithout the (AR) condition. Complex Variables and Elliptic Equations, Vol. 61, Issue. 11, p. 1481.

    Xu, Fei Gao, Yixian Yang, Xue and Zhang, He 2017. Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method. Mathematical Problems in Engineering, Vol. 2016, p. 1.

    Yin, Rong Zhang, Jihui and Shang, Xudong 2017. The overdetermined equations on bounded domain. Complex Variables and Elliptic Equations, Vol. 61, Issue. 11, p. 1566.

    Zhang, Xia and Zhang, Chao 2017. Existence of solutions for critical fractional Kirchhoff problems. Mathematical Methods in the Applied Sciences,


Book description

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

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