Multiple solutions for resonant problems of the Robin p-Laplacian plus an indefinite potential View Full Text


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Article Info

DATE

2017-04-25

AUTHORS

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

ABSTRACT

We study a nonlinear boundary value problem driven by the p-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carathéodory function which is asymptotically resonant at ±∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm \infty $$\end{document} with respect to a nonprincipal Ljusternik–Schnirelmann eigenvalue. Using variational methods, together with Morse theory and truncation-perturbation techniques, we show that the problem has at least three nontrivial smooth solutions, two of which have a fixed sign. More... »

PAGES

63

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00526-017-1164-2

DOI

http://dx.doi.org/10.1007/s00526-017-1164-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1085055764


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