Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONTRIVIAL SOLUTIONS FOR THE NONLINEAR BIHARMONIC SYSTEM WITH DIRICHLET BOUNDARY CONDITION

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2010.11.16
  • Accepted : 2010.12.15
  • Published : 2010.12.30
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Abstract

We investigate the existence of multiple nontrivial solutions (${\xi}$, ${\eta}$) for perturbations $g_1$, $g_2$ of the harmonic system with Dirichlet boundary condition $${\Delta}^2{\xi}+c{\Delta}{\xi}=g_1(2{\xi}+3{\eta})\;in\;{\Omega}\\{\Delta}^2{\eta}+c{\Delta}{\eta}=g_2(2{\xi}+3{\eta})\;in\;{\Omega}$$ where we assume that ${\lambda}_1$ < $c$ < ${\lambda}_2$, $g^{\prime}_1({\infty})$, $g^{\prime}_2({\infty})$ are finite. We prove that the system has at least three solutions under some condition on $g$.

Keywords

References

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