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On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term. (English) Zbl 0665.35050
This paper proves that there exists a positive integer T such that the semilinear wave equation $u_{tt}-u_{xx}+f(x,t,u)=0$ has a $$2\pi$$ /T-periodic solution if the forcing term satisfies the following conditions: (1) continuity; (2) periodicity: $$f(x,t+2\pi /T,u)=f(x,t,u)$$, $$x\in [0,\pi]$$, $$t,u\in R'$$; (3) monotonicity, $$f(x,t,u_ 2)\geq f(x,t,u_ 1)$$ if $$u_ 2\geq u_ 1$$, for $$x\in [0,\pi]$$, $$t\in R^ 1$$; (4) growth condition.
Reviewer: J.H.Tian

##### MSC:
 35L70 Second-order nonlinear hyperbolic equations 35B10 Periodic solutions to PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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##### References:
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