Existence and multiplicity of solutions for resonant-superlinear problems

Abstract

We consider a semilinear Dirichlet problem with a reaction which exhibits an asymmetric behaviour as x →±∞ (it is superlinear as x →+∞ and resonant as x →−∞). Using variational tools from the critical point theory, together with truncation and comparison techniques and critical groups, we prove two multiplicity theorems producing two and three nontrivial solutions. Also we show that the problem can not have negative solutions.