Dirichlet Problems with an Indefinite and Unbounded Potential and Concave‐Convex Nonlinearities
Copyright policy )Dirichlet Problems with an Indefinite and Unbounded Potential and Concave‐Convex Nonlinearities
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) 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 solutions, and in the second theorem we provide precise sign information for all the solutions.
Variational methods for second-order elliptic equations, parametric semilinear Dirichlet problem, Boundary value problems for second-order elliptic equations, QA1-939, variational method, Mathematics
Variational methods for second-order elliptic equations, parametric semilinear Dirichlet problem, Boundary value problems for second-order elliptic equations, QA1-939, variational method, Mathematics
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