Multiple stationary solutions to gkp equation in a bounded domain Report as inadecuate




Multiple stationary solutions to gkp equation in a bounded domain - Download this document for free, or read online. Document in PDF available to download.



In this paper, we study the existence of multiple stationarysolutions of Generalized Kadomtsev-Petviashvili Abbr. GKP equation in a bounded domain with smooth boundary and for superlinear nonlinear term fu = L|u|p-2u |u|q-2u  where 1

Tipo de documento: Artículo - Article

Palabras clave: GKP equation, Stationary solution, Symmetric Mountain Pass Lemma, Kransnoselskii genus





Source: http://www.bdigital.unal.edu.co


Teaser



Boletı́n de Matemáticas Nueva Serie, Volumen IX No.
1 (2002), pp.
11–22 MULTIPLE STATIONARY SOLUTIONS TO GKP EQUATION IN A BOUNDED DOMAIN BENJIN XUAN (*) Abstract.
In this paper, we study the existence of multiple stationary solutions of Generalized Kadomtsev-Petviashvili (Abbr.
GKP) equation in a bounded domain with smooth boundary and for superlinear nonlinear term f (u) = λ|u|p−2 u |u|q−2 u where 1 ≤ p, q 2∗ = 2(2n−1) . 2n−3 Our methods are based on variational methods, and the results are divided into two cases according to the different values of the parameters p, q. Key words and phrases.
GKP equation, Stationary solution, Symmetric Mountain Pass Lemma, Kransnoselskii genus 2000 Mathematics Subject Classification: 35J60. 1.
Introduction. Kadomtsev-Petviashvili equation and its generalization appear in many advances in Physics (cf.
[3], [4], [5], [7], [9], [10] and the references therein). Generally, it reads (1) wt wxxx (f (w))x = Dx−1 ∆y w, (*) Supported by Grant 10071080 and 10101024 from the NNSF of China. Department of Mathematics Universidad Nacional de Colombia University of Science and Technology of China e-mail:bjxuan@matematicas.unal.edu.co. 11 12 BENJIN XUAN where (t, x, y) ∈ R × R × Rn−1 , n ≥ 2, Dx−1 h(x, y) = ∂2 ∂y12 ∂2 ∂y22 ··· Rx ∂2 . 2 ∂yn−1 −∞ h(s, y)ds, ∆y := In [4] and [5], using the constrained minimization method, De Bouard and Saut obtained the existence and nonexistence of solitary waves in the case where the power nonlinearities are f (u) = up , p = k-l, with k, l relatively prime and l is odd.
In the Chapter 7 of [9], Willem extended the results of [4] to the case where n = 2, f (u) is a continuous function satisfying some structure conditions.
In paper [10], we extended the results of [4], [5] and [9] to higher dimensional spaces for a more general nonlinearity f (u) which satisfies some structure conditions. In this paper, we shall investigate ...






Related documents