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)
  • 투고 : 2010.11.16
  • 심사 : 2010.12.15
  • 발행 : 2010.12.30

초록

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 $g$.

키워드

참고문헌

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