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.
Citation
Pavel Drábek. "Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results." Topol. Methods Nonlinear Anal. 25 (1) 183 - 194, 2005.
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