Existence and multiplicity of solutions for resonant (p,2)-equations

الأصل · EN

We consider Dirichlet elliptic equations driven by the sum of a p-Laplacian (2<p) and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both ±∞ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.