Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results
Słowa kluczowe
p-Laplacian, Fredholm alternative, bifurcation, asymptotic estimatesAbstrakt
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.Pobrania
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2005-03-01
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1.
DRÁBEK, Pavel. Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results. Topological Methods in Nonlinear Analysis [online]. 1 marzec 2005, T. 25, nr 1, s. 183–194. [udostępniono 22.7.2024].
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