Search results for "Truncation and comparison"
showing 2 items of 2 documents
Singular Neumann (p, q)-equations
2019
We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.
Positive solutions for nonlinear Robin problems
2017
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.