Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 34, Number 1 (2009), 111-130.
On a $p$-superlinear Neumann $p$-Laplacian equation
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).
Topol. Methods Nonlinear Anal., Volume 34, Number 1 (2009), 111-130.
First available in Project Euclid: 27 April 2016
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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