×

The forced vibrations on a class of nonlinear wave equations. (Chinese. English summary) Zbl 0663.35044

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

Citations:

Zbl 0178.453
PDFBibTeX XMLCite