Bai, Donghua The forced vibrations on a class of nonlinear wave equations. (Chinese. English summary) Zbl 0663.35044 J. Sichuan Univ., Nat. Sci. Ed. 1987, No. 3, 241-249 (1987). The existence of time periodic solutions of a nonlinear wave equation \(v_{tt}-v_{\bar x\bar x}+F(t,x,u)=0\) with Dirichlet boundary conditions on a finite interval is given. We assume essentially that F satisfies the same conditions as in O. Vejvoda [Czech. Math. J. 14(89), 341-379 (1964; Zbl 0178.453)] where the free term is \(\epsilon\) F with a small parameter \(\epsilon\). MSC: 35L70 Second-order nonlinear hyperbolic equations 35B10 Periodic solutions to PDEs 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B20 Perturbations in context of PDEs Keywords:existence; time periodic solutions; nonlinear wave equation; Dirichlet boundary conditions; finite interval; small parameter Citations:Zbl 0178.453 PDFBibTeX XMLCite \textit{D. Bai}, J. Sichuan Univ., Nat. Sci. Ed. 1987, No. 3, 241--249 (1987; Zbl 0663.35044)