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ASYMPTOTICALLY LINEAR ELLIPTIC SYSTEMS WITH PARAMETERS

Published online by Cambridge University Press:  29 March 2010

CHAOQUAN PENG
CHAOQUAN PENG*
Affiliation:
Department of Mathematics, South-Central University for Nationalities, Wuhan 430074, The People's Republic of China e-mail: pcq1979@163.com
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Abstract

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In this paper, we show that the semi-linear elliptic systems of the form(0.1)\begin{equation} \left\{ \arraycolsep=1.5pt \begin{array}{lll} -\Delta u-\mu\Delta v=g(x,v), \quad -\Delta v-\lambda\Delta u=f(x,u), & x\in \Omega,\\[2pt] u=v=0, & x\in \partial \Omega \end{array} \right. \end{equation}possess at least one non-trivial solution pair (u, v) ∈ H01(Ω) × H01(Ω), where Ω is a smooth bounded domain in ℝN, λ and μ are non-negative numbers, f(x, t) and g(x, t) are continuous functions on Ω × ℝ and asymptotically linear at infinity.

Keywords

AMS classification: 35J6035J65

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 383 - 389
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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