Constant sign and nodal solutions for a class of nonlinear Dirichlet problems

• Autor(a) principal: Papageorgiou, N. S.
• Data de Publicação: 2015
• Outros Autores: Santos, S. R. Andrade, Staicu, V.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/14982
• topic: Mountain pass theorem; Second deformation theorem; Eigenvalues of p-Laplacian; Critical groups; Constant sign and nodal solutions; Extremal solutions

We consider a nonlinear Dirichlet problem with a Carathéodory reaction which has arbitrary growth from below. We show that the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal. In the semilinear case (i.e., p =2), with the reaction f(z, .)being C1and with subcritical growth, we show that there is a second nodal solution, for a total of four nontrivial smooth solutions. Finally,when the reaction has concave terms and is subcritical and for the nonlinear problem (i.e., 1 <p <∞) we show that again we can have the existence of three nontrivial smooth solutions, two of constant sign and a third nodal.