Ren, Lishun; An, Yukun An existence result for a system of semilinear beam equations with damping at nonresonance. (Chinese. English summary) Zbl 1028.35112 Math. Appl. 14, No. 2, 52-55 (2001). 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. MSC: 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 Keywords:periodic-Dirichlet boundary value problem; semilinear beam equations; Lyapunov-Schmidt reduction method; Leray-Schauder fixed point theorem PDF BibTeX XML Cite \textit{L. Ren} and \textit{Y. An}, Math. Appl. 14, No. 2, 52--55 (2001; Zbl 1028.35112)