Topological Methods in Nonlinear Analysis

Existence of multiple solutions for a quasilinear elliptic problem

Jorge Cossio, Sigifredo Herrón, and Carlos Vélez

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Abstract

In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the $p$-derivative at zero and the $p$-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the $p$-Laplace operator. Our proof uses bifurcation from infinity and bifurcation from zero to prove the existence of unbounded branches of positive solutions (resp. of negative solutions). We show the existence of multiple solutions and we provide qualitative properties of these solutions.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 50, Number 2 (2017), 531-551.

Dates
First available in Project Euclid: 11 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1507687546

Digital Object Identifier
doi:10.12775/TMNA.2017.019

Mathematical Reviews number (MathSciNet)
MR3747027

Zentralblatt MATH identifier
06836832

Citation

Cossio, Jorge; Herrón, Sigifredo; Vélez, Carlos. Existence of multiple solutions for a quasilinear elliptic problem. Topol. Methods Nonlinear Anal. 50 (2017), no. 2, 531--551. doi:10.12775/TMNA.2017.019. https://projecteuclid.org/euclid.tmna/1507687546


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