A nonlinear beam equation with nonlinearity crossing an eigenvalue

Q-Heung Choi; Hyewon Nam

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J. Korean Math. Soc. 1997; 34(3): 609-622

Printed September 1, 1997

A nonlinear beam equation with nonlinearity crossing an eigenvalue

Q-Heung Choi and Hyewon Nam

Inha university and Inha university

Abstract

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Abstract

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $(- {\frac{\pi}{2}} , {\frac{\pi}{2}} )$ and periodic condition on the varible $t$, $Lu + bu^+ - au^- = f(x,t)$, when the jumping nonlinearity crosses the first positive eigenvalue.

Keywords: eigenvalue, beam equation, multiplicity of solutions

MSC numbers: 35B10, 35Q40