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

Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu

DOI: http://dx.doi.org/10.12775/TMNA.2009.032


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).


p-superlinearity; mountain pass theorem; C-condition; Morse theory; critical groups

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