THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN

Diego Averna; Gabriele Bonanno

doi:10.1017/S0013091502000767

Abstract

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In this paper we prove the existence of at least three classical solutions for the problem

$$ \left\{ \begin{aligned} \amp-(|u'|^{p-2}u')'=\lambda f(t,u)h(u'), \\ \ampu(a)=u(b)=0, \end{aligned} \right. $$

when $\lambda$ lies in an explicitly determined open interval.

Our main tool is a very recent three-critical-points theorem stated in a paper by D. Averna and G. Bonanno (Topolog. Meth. Nonlin. Analysis22 (2003), 93–103).

AMS 2000 Mathematics subject classification: Primary 34B15

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Averna, Diego and Salvati, Roberta 2004. Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian. Journal of Mathematical Analysis and Applications, Vol. 298, Issue. 1, p. 245.

Bonanno, Gabriele 2004. Multiple critical points theorems without the Palais–Smale condition. Journal of Mathematical Analysis and Applications, Vol. 299, Issue. 2, p. 600.

2005. Half-Linear Differential Equations. Vol. 202, Issue. , p. 471.

Candito, Pasquale 2006. Two solutions to a nonlinear Neumann problem without asymptotic conditions. Rendiconti del Circolo Matematico di Palermo, Vol. 55, Issue. 1, p. 43.

Tian, Yu and Ge, Weigao 2007. Multiple solutions for certain nonlinear second-order systems. Journal of Applied Mathematics and Computing, Vol. 25, Issue. 1-2, p. 353.

Tian, Yu and Ge, Weigao 2008. Second-Order Sturm-Liouville Boundary Value Problem Involving the One-Dimensional $p$-Laplacian. Rocky Mountain Journal of Mathematics, Vol. 38, Issue. 1,

Averna, Diego and Bonanno, Gabriele 2009. A Mountain Pass Theorem for a Suitable Class of Functions. Rocky Mountain Journal of Mathematics, Vol. 39, Issue. 3,

Tian, Yu and Ge, Weigao 2009. Multiple Positive Solutions for a Second Order Sturm-Liouville Boundary Value Problem with a $p$-Laplacian via Variational Methods. Rocky Mountain Journal of Mathematics, Vol. 39, Issue. 1,

Tian, Yu and Ge, Weigao 2010. Multiple Positive Solutions of Second-Order Sturm-Liouville Boundary Value Problems for Impulsive Differential Equations. Rocky Mountain Journal of Mathematics, Vol. 40, Issue. 2,

Tian, Yu and Ge, Weigao 2011. Sign-changing and multiple solutions of the Sturm–Liouville boundary value problem via invariant sets of descending flow. Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue. 16, p. 5480.

Tian, Yu and Ge, Weigao 2011. Multiple solutions of Sturm–Liouville boundary value problem via lower and upper solutions and variational methods. Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue. 17, p. 6733.

Graef, John R. Heidarkhani, Shapour and Kong, Lingju 2012. A critical points approach for the existence of multiple solutions of a Dirichlet quasilinear system. Journal of Mathematical Analysis and Applications, Vol. 388, Issue. 2, p. 1268.

Graef, John R. Heidarkhani, Shapour and Kong, Lingju 2014. Infinitely Many Solutions for Systems of Sturm–Liouville Boundary Value Problems. Results in Mathematics, Vol. 66, Issue. 3-4, p. 327.

Shokooh, S. Afrouzi , G. A. and Hadjian, A. 2020. On the existence of solutions of one-dimensional fourth-order equations. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, Issue. 11, p. 1575.

Heidarkhani, Shapour Afrouzi, Ghasem A. and Moradi, Shahin 2021. Variational approaches to systems of Sturm–Liouville boundary value problems. Asian-European Journal of Mathematics, Vol. 14, Issue. 03, p. 2150032.

Shokooh, S. Afrouzi, G. A. and Hadjian, A. 2021. On The Existence of Solutions to One-Dimensional Fourth-Order Equations. Ukrainian Mathematical Journal, Vol. 72, Issue. 11, p. 1820.

Bonanno, G. D’Aguì, G. and Sciammetta, A. 2023. Multiple solutions for a class of anisotropic p⃗-Laplacian problems. Boundary Value Problems, Vol. 2023, Issue. 1,

HADJİAN, Armin and NİETO, Juan 2023. Existence results for a Dirichlet boundary value problem through a local minimization principle. Hacettepe Journal of Mathematics and Statistics, Vol. 52, Issue. 1, p. 126.

Article contents

THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN

Abstract

Keywords

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