Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results
Keywords
p-Laplacian, Fredholm alternative, bifurcation, asymptotic estimatesAbstract
In this paper we address the existence and multiplicity results for $$ \cases -\Delta_p u -\lambda |u|^{p-2} u = h (x,u) &\text{in }\Omega, \\ u = 0 &\text{on } \partial \Omega, \endcases $$ where $p> 1$, $\Delta_p u = \text{\rm div}(|\nabla u|^{p-2}\nabla u)$, $h$ 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.Downloads
Published
2005-03-01
How to Cite
1.
DRÁBEK, Pavel. Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results. Topological Methods in Nonlinear Analysis. Online. 1 March 2005. Vol. 25, no. 1, pp. 183 - 194. [Accessed 25 September 2024].
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