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

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

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We consider a parametric semilinear Dirichlet 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) vivobook x515 term.Using variational methods coupled with suitable truncation techniques, we prove two multiplicity theorems for small values of the parameter.Both theorems produce five nontrivial smooth 15-eg1053cl solutions, and in the second theorem we provide precise sign information for all the solutions.