INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES

Pasquale Candito

doi:10.1017/S0013091501000189

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we establish the existence of infinitely many solutions to a Neumann problem involving the p-Laplacian and with discontinuous nonlinearities. The technical approach is mainly based on a very recent result on critical points for possibly non-smooth functionals in a Banach space due to Marano and Motreanu, namely Theorem 1.1 in a paper that is to appear in the journal J. Diff. Eqns (see Theorem 2.3 in the body of this paper). Some applications are presented.

AMS 2000 Mathematics subject classification: Primary 35A15; 35J65; 35R05

Crossref Citations

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

Bonanno, Gabriele and Candito †, Pasquale 2004. On a class of nonlinear variational–hemivariational inequalities. Applicable Analysis, Vol. 83, Issue. 12, p. 1229.

Anello, Giovanni 2004. Existence of infinitely many weak solutions for a Neumann problem. Nonlinear Analysis: Theory, Methods & Applications, Vol. 57, Issue. 2, p. 199.

Marano, Salvatore A. and Bisci, Giovanni Molica 2006. Multiplicity results for a Neumann problem withp-Laplacian and non-smooth potential. Rendiconti del Circolo Matematico di Palermo, Vol. 55, Issue. 1, p. 113.

Kristály, Alexandru 2006. Infinitely many solutions for a differential inclusion problem inRN. Journal of Differential Equations, Vol. 220, Issue. 2, p. 511.

Ricceri, Biagio 2007. Open Problems in Topology II. p. 585.

Hu, Shouchuan and Papageorgiou, Nikolaos S. 2007. Neumann problems for nonlinear hemivariational inequalities. Mathematische Nachrichten, Vol. 280, Issue. 3, p. 290.

Kristály, Alexandru and Motreanu, Dumitru 2007. Nonsmooth Neumann-Type Problems Involving thep-Laplacian. Numerical Functional Analysis and Optimization, Vol. 28, Issue. 11-12, p. 1309.

Bonanno, Gabriele and D'Aguì, Giuseppina 2009. On the Neumann problem for elliptic equations involving the p-Laplacian. Journal of Mathematical Analysis and Applications, Vol. 358, Issue. 2, p. 223.

Bonanno, Gabriele and D’Aguì, Giuseppina 2009. A Neumann boundary value problem for the Sturm–Liouville equation. Applied Mathematics and Computation, Vol. 208, Issue. 2, p. 318.

Ricceri, Biagio 2010. A note on the Neumann problem. Complex Variables and Elliptic Equations, Vol. 55, Issue. 5-6, p. 593.

Bonanno, Gabriele Motreanu, Dumitru and Winkert, Patrick 2011. Variational–hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions. Journal of Mathematical Analysis and Applications, Vol. 381, Issue. 2, p. 627.

Shoorabi, Davood Maghsoodi and Afrouzi, Ghasem Alizadeh 2012. Infinitely many solutions for class of Neumann quasilinear elliptic systems. Boundary Value Problems, Vol. 2012, Issue. 1,

Afrouzi, Ghasem A. and Hadjian, Armin 2013. Infinitely many solutions for a Dirichlet boundary value problem depending on two parameters. Glasnik Matematicki, Vol. 48, Issue. 2, p. 357.

Heidarkhani, Shapour 2014. Infinitely many solutions for systems of n fourth order partial differential equations coupled with Navier boundary conditions. Arab Journal of Mathematical Sciences, Vol. 20, Issue. 1, p. 77.

Lu, Feng-Yun and Deng, Gui-Qian 2014. Infinitely Many Weak Solutions of thep-Laplacian Equation with Nonlinear Boundary Conditions. The Scientific World Journal, Vol. 2014, Issue. , p. 1.

Heidarkhani, Shapour and Henderson, Johnny 2014. INFINITELY MANY SOLUTIONS FOR A PERTURBED QUASILINEAR TWO-POINT BOUNDARY VALUE PROBLEM. Annals of the Alexandru Ioan Cuza University - Mathematics, Vol. 0, Issue. 0,

Shokooh, Saeid Afrouzi, Ghasem A. and Zahmatkesh, Hossain 2018. Infinitely many weak solutions for fourth-order equations depending on two parameters. Boletim da Sociedade Paranaense de Matemática, Vol. 36, Issue. 4, p. 131.

Khademloo, S. Afrouzi, G. A. and Ghara, T. Norouzi 2018. Infinitely many solutions for anisotropic variable exponent problems. Complex Variables and Elliptic Equations, Vol. 63, Issue. 9, p. 1353.

Averna, Diego Sciammetta, Angela and Tornatore, Elisabetta 2018. Infinitely many solutions to boundary value problem for fractional differential equations. Fractional Calculus and Applied Analysis, Vol. 21, Issue. 6, p. 1585.

Kim, Jae-Myoung 2019. Elliptic problems involving the p-Laplacian in ℝN with locally Lipschitz functional. Complex Variables and Elliptic Equations, Vol. 64, Issue. 3, p. 361.

Download full list

Article contents

INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES

Abstract

Keywords

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

Article contents

INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES

Abstract

Keywords

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests