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Title: Constant sign and nodal solutions for a class of nonlinear Dirichlet problems
Author: Papageorgiou, N. S.
Santos, S. R. Andrade
Staicu, V.
Keywords: Mountain pass theorem
Second deformation theorem
Eigenvalues of p-Laplacian
Critical groups
Constant sign and nodal solutions
Extremal solutions
Issue Date: Feb-2015
Publisher: Elsevier
Abstract: 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.
Peer review: yes
DOI: 10.1016/j.jmaa.2014.08.041
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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