Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A WEAK SOLUTION OF A NONLINEAR BEAM EQUATION

  • Choi, Q.H. (Department of Mathematics Inha University) ;
  • Choi, K.P. (Department of Mathematics Inha University) ;
  • Jung, T. (Department of Mathematics Kunsan National University) ;
  • Han, C.H. (Department of Civil Engineering Kangweon National University)
  • Received : 1995.12.07
  • Published : 1996.03.15
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Abstract

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.

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