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Title: Nonlinear Robin problems with locally defined reaction
Author: Aizicovici, Sergiu
Papageorgiou, Nikolaos S.
Staicu, Vasile
Keywords: Cut-off function
Extremal constant sign solutions
Regularity theory
Issue Date: 2023
Publisher: Yokohama publishers
Abstract: We consider a nonlinear Robin problem driven by a p− Laplacian. The reaction consistes of two terms. The first one is parametric and only locally defined, while the second one is (p − 1)- superlinear. Using cutt-off techniques together with critical point theory and critical groups, we show that for big values of the parameter λ > 0, the problem has at least three nontrivial solutions, all with sign information (positive, negative and nodal). In the semilinear case (p = 2), we produce a second nodal solution, for a total of four nontrivial solutions, all with sign information.
Peer review: yes
ISSN: 2189-3754
Publisher Version:
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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