Topological Methods in Nonlinear Analysis

On a $p$-superlinear Neumann $p$-Laplacian equation

Abstract

We 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).

Article information

Source
Topol. Methods Nonlinear Anal., Volume 34, Number 1 (2009), 111-130.

Dates
First available in Project Euclid: 27 April 2016

https://projecteuclid.org/euclid.tmna/1461785687

Mathematical Reviews number (MathSciNet)
MR2581462

Zentralblatt MATH identifier
1183.35099

Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. On a $p$-superlinear Neumann $p$-Laplacian equation. Topol. Methods Nonlinear Anal. 34 (2009), no. 1, 111--130. https://projecteuclid.org/euclid.tmna/1461785687

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