Nonlinear elliptic problems with superlinear reaction and parametric concave boundary condition

摘要

We study parametric nonlinear elliptic boundary value problems driven by the p-Laplacian with convex and concave terms. The convex term appears in the reaction and the concave in the boundary condition (source). We study the existence and nonexistence of positive solutions as the parameter lambda > 0 varies. For the semilinear problem (p = 2), we prove a bifurcation type result. Finally, we show the existence of nodal (sign changing) solutions.