Topological Methods in Nonlinear Analysis

Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results

Pavel Drábek

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Abstract

In this paper we address the existence and multiplicity results for $$ \begin{cases} -\Delta_p u -\lambda |u|^{p-2} u = h (x,u) &\text{in }\Omega, \\ u = 0 &\text{on } \partial \Omega, \end{cases} $$ where $p> 1$, $\Delta_p u = {\rm div}(|\nabla u|^{p-2}\nabla u)$, $h$ is a bounded function and the spectral parameter $\lambda$ stays "near" the principal eigenvalue of the $p$-Laplacian.

We show how the bifurcation theory combined with certain asymptotic estimates yield desired results.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 25, Number 1 (2005), 183-194.

Dates
First available in Project Euclid: 23 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1466705101

Mathematical Reviews number (MathSciNet)
MR2133398

Zentralblatt MATH identifier
1091.35052

Citation

Drábek, Pavel. Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results. Topol. Methods Nonlinear Anal. 25 (2005), no. 1, 183--194. https://projecteuclid.org/euclid.tmna/1466705101


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