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Title: Nodal and multiple solutions for nonlinear periodic problems with competing nonlinearities
Author: Aizicovicim, S.
Papageorgiou, N. S.
Staicu, Vasile
Keywords: Nonhomogeneous differential operator
Nonlinear strong maximum principle
Concave and convex nonlinearities
Multiple and nodal solutions
Critical groups
Issue Date: 2013
Publisher: World Scientific
Abstract: We consider a nonlinear periodic problem drive driven by a nonhomogeneous differential operator which incorporates as a special case the scalar p-Laplacian, and a reaction which exhibits the competition of concave and convex terms. Using variational methods based on critical point theory, together with suitable truncation techniques and Morse theory (critical groups), we establish the existence of five nontrivial solutions, two positive, two negative and the fifth nodal (sign-changing). In the process, we also prove some auxiliary results of independent interest.
Peer review: yes
DOI: 10.1142/S0219199713500016
ISSN: 1793-6683
Appears in Collections:CIDMA - Artigos

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