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

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

#### 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).

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).

#### Keywords

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

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.