On the high energy solitary waves solutions for a generalized KP equation  in bounded domain

Jebari Rochdi

doi:10.37863/umzh.v74i3.6253

Jebari Rochdi Dep. Math., College Sci. and Humanities-Al Quwayiyah, Shaqra Univ., Riyadh, Kingdom of Saudi Arabia; Dep. Math., Faculte Sci. Tunis, Univ. Tunis El-Manar, Tunisie

DOI: https://doi.org/10.37863/umzh.v74i3.6253

Keywords: Generalized KP equation, variant fountain theorems, variational methods, infinitely many high energy solitary waves solutions.

Abstract

UDC 517.9

We are mainly concerned with the existence of infinitely many high energy solitary waves solutions for a class of generalized Kadomtsev – Petviashvili equation (KP equation) in bounded domain. The aim of this paper is to fill the gap in the relevant literature stated in a previous paper (J. Xu, Z. Wei, Y. Ding, Stationary solutions for a generalized Kadomtsev – Petviashvili equation in bounded domain, Electron. J. Qual. Theory Differ. Equ., 2012, № 68, 1 – 18 (2012)). Under more relaxed assumption on the nonlinearity involved in KP equation, we obtain a new result on the existence of infinitely many high energy solitary waves solutions via a variant fountain theorems.

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