Large Amplitude Time Periodic Solutions of a Semilinear Wave Equation.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This paper studies the existence of periodic solutions for a family of semilinear wave equations where the restoring force is independent of time, monotone, and grows at a more rapid rate than linear near infinity. With appropriate technical assumptions it is shown that there is an unbounded sequence of such free vibrations, i.e. there are solutions of arbitrarily large amplitude. If the restoring force is independent of x, the monotonicity assumption can be omitted.
- Numerical Mathematics