Topological Methods in Nonlinear Analysis

Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results

Pavel Drábek

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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.

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

First available in Project Euclid: 23 June 2016

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Drábek, Pavel. Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results. Topol. Methods Nonlinear Anal. 25 (2005), no. 1, 183--194.

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