On a $p$-superlinear Neumann $p$-Laplacian equation
Keywordsp-superlinearity, mountain pass theorem, C-condition, Morse theory, critical groups
AbstractWe consider a nonlinear Neumann problem, driven by the $p$-Laplacian, and with a nonlinearity which exhibits a $p$-superlinear growth near infinity, but does not necessarily satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on critical point theory, together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions, of which two have a fixed sign (one positive and the other negative).
How to Cite
AIZICOVICI, Sergiu, PAPAGEORGIOU, Nikolaos S. & STAICU, Vasile. On a $p$-superlinear Neumann $p$-Laplacian equation. Topological Methods in Nonlinear Analysis [online]. 1 September 2009, T. 36, nr 1, s. 111–130. [accessed 1.12.2021].
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