Publication Cover
Applicable Analysis
An International Journal
Volume 82, 2003 - Issue 11
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Original Articles

Nontrivial stationary solutions to GKP equation in bounded domain

Pages 1039-1048 | Received 05 Jun 2002, Accepted 18 Mar 2003, Published online: 12 May 2010
 

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.

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