Abstract
In this article, using the Mountain Pass Lemma due to Ambrosetti and Rabinowitz, we obtain the existence of nontrivial stationary solutions of Generalized Kadomtsev–Petviashvili (GKP) equation in a bounded domain with smooth boundary and for superlinear nonlinear term f (u) which satisfies some growth condition. Based on a Pohozaev type variational identity for cylindrical symmetric solution, we obtain the nonexistence of the nontrivial cylindrical symmetric solution for super-critical nonlinearity, i.e. f(u)=|u| p −2 u where .
Acknowledgment
The author was supported by Grant 10071080 and 10101024 from the NNSF of China.