ABSTRACT
We consider a semilinear Dirichlet problem with a reaction which exhibits an asymmetric behaviour as (it is superlinear as and resonant as ). 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.
Acknowledgments
The authors thank the anonymous reviewers for their careful reading of the manuscript and their comments and suggestions. All authors contribute equally to this paper. All authors read and approved the final manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).