Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

Blog Article

We consider a parametric semilinear Dirichlet Basketball - Balls problem with an unbounded and indefinite potential.In the reaction we have the competing effects of a sublinear (concave) term and of a superlinear (convex) term.Using variational methods coupled with suitable truncation techniques, we prove two multiplicity Toilet Paper Stand theorems for small values of the parameter.Both theorems produce five nontrivial smooth solutions, and in the second theorem we provide precise sign information for all the solutions.