Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONTRIVIAL SOLUTIONS FOR AN ELLIPTIC SYSTEM

  • Received : 2014.12.02
  • Accepted : 2015.03.16
  • Published : 2015.03.30
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Abstract

In this work, we consider an elliptic system $$\left{\array {-{\Delta}u=au+bv+{\delta}_1u+-{\delta}_2u^-+f_1(x,u,v) && in\;{\Omega},\\-{\Delta}v=bu+cv+{\eta}_1v^+-{\eta}_2v^-+f_2(x,u,v) && in\;{\Omega},\\{\hfill{70}}u=v=0{\hfill{90}}on\;{\partial}{\Omega},}$$, where ${\Omega}{\subset}R^N$ 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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Acknowledgement

Supported by : Namseoul University

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