We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.
Degiovanni, M., Lancelotti, S., Perera, K., Nontrivial solutions of p-superlinear p-Laplacian problems via a cohomological local splitting, <<COMMUNICATIONS IN CONTEMPORARY MATHEMATICS>>, 2010; 12 (3): 475-486. [doi:10.1142/S0219199710003890] [http://hdl.handle.net/10807/2974]
Nontrivial solutions of p-superlinear p-Laplacian problems via a cohomological local splitting
Degiovanni, Marco;Lancelotti, Sergio;
2010
Abstract
We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.
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