EXISTENCE, NONEXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR PARAMETRIC NONLINEAR ELLIPTIC EQUATIONS

We consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter lambda varies in R-0(+) of and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p - 1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p - 1)-linear.