Topological structure of the solution set of singular equations with sign changing terms under Dirichlet boundary condition

José Valdo Gonçalves, Marcos R. Marcial, Olimpio H. Miyagaki

DOI: http://dx.doi.org/10.12775/TMNA.2015.091

Abstract


In this paper we establish existence of connected components of positive solutions of the equation $ -\Delta_{p} u = \lambda f(u)$ in~$\Omega$, under Dirichlet boundary conditions, where $\Omega \subset \R^N$ is a~bounded domain with smooth boundary $\partial\Omega$, $\Delta_{p}$ is the $p$-Laplacian, and $f \colon (0,\infty) \rightarrow {\R} $ is a continuous function which may blow up to $\pm \infty$ at the origin.

Keywords


Connected sets; fixed points; Schauder theory; elliptic equations

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