We consider nonlinear Neumann problems driven by the p–Laplacian plus an indefinite potential and with a superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. First we prove an existence theorem and then under stronger conditions on the reaction, we prove a multiplicity theorem producing three nontrivial solutions. Then, we examine parametric problems with competing nonlinearities (concave and convex terms). We show that for all small values of the parameter λ > 0, the problem has five nontrivial solutions and if p = 2 (semilinear equation), there are six nontrivial solutions. Finally, we prove a bifurcation result describing the set of positive solutions as the parameter λ > 0 varies.
Superlinear Neumann problems with the p-Laplacian plus an indefinite potential
MUGNAI, Dimitri;
2017
Abstract
We consider nonlinear Neumann problems driven by the p–Laplacian plus an indefinite potential and with a superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. First we prove an existence theorem and then under stronger conditions on the reaction, we prove a multiplicity theorem producing three nontrivial solutions. Then, we examine parametric problems with competing nonlinearities (concave and convex terms). We show that for all small values of the parameter λ > 0, the problem has five nontrivial solutions and if p = 2 (semilinear equation), there are six nontrivial solutions. Finally, we prove a bifurcation result describing the set of positive solutions as the parameter λ > 0 varies.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
