Topological structure of the solution set of singular equations with sign changing terms under Dirichlet boundary condition
J.V. Gonçalves, M. R. Marcial, Olı́mpio H. Miyagaki · Topological Methods in Nonlinear Analysis · 2015
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.