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



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.


Connected sets; fixed points; Schauder theory; elliptic equations

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