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An existence result for a system of semilinear beam equations with damping at nonresonance. (Chinese. English summary) Zbl 1028.35112
Summary: This paper deals with the periodic-Dirichlet boundary value problem for the system of semilinear beam equations with damping \(u_{tt}+ u_{xxxx}+ Bu_t= Au+ g(t, x,u)+ h(t,x)\). Using the Lyapunov-Schmidt reduction method together with the Leray-Schauder fixed point theorem existence of a solution for this system under suitable conditions is obtained.
35L75 Higher-order nonlinear hyperbolic equations
35L35 Initial-boundary value problems for higher-order hyperbolic equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35B34 Resonance in context of PDEs