Korean J. Math. Vol. 23 No. 1 (2015) pp.153-161
DOI: https://doi.org/10.11568/kjm.2015.23.1.153

Nontrivial solutions for an elliptic system

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Published: Mar 30, 2015
Keywords:
Elliptic system, Linking inequality
Mathematics Subject Classification:
35J55, 49J35

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Hyewon Nam
Department of General Education Namseoul University Chonam, 330-707 Korea
Seong Cheol Lee
Department of General Education Namseoul University Chonam, 330-707 Korea

Abstract

In this work, we consider an elliptic system
{−△u=au+bv+δ1u+−δ2u−+f1(x,u,v) in Ω,−△v=bu+cv+η1v+−η2v−+f2(x,u,v) in Ω,u=v=0 on ∂Ω,
where Ω⊂RN be a bounded domain with smooth
boundary. We prove that the system has at least
two nontrivial solutions by applying linking theorem.



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Supporting Agencies

This work was supported by Namseoul University

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