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manuscripta mathematica

, Volume 5, Issue 2, pp 165–194 | Cite as

Time periodic solutions of nonlinear wave equations

  • Paul H. Rabinowitz
Article

Abstract

Existence and regularity of solutions of
$$(1)u_{tt} - u_{xx} = \varepsilon K(x,t,u,u_t )0< x< \pi ,0 \leqslant t \leqslant 2\pi $$
together with the periodicity and boundary conditions
$$(2)u(x,t + 2\pi ) = u(x,t),u(0,t) = 0 = u(\pi ,t)$$
is studied both with an without the dissipation ut. A solution is a pair (χ, u). A main feature of interest here is an infinite dimensional biofurcation problem. Under appropriate conditions on K, global existence results are obtained by a combination of analytical and topological methods.

Keywords

Boundary Condition Wave Equation Periodic Solution Number Theory Algebraic Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Paul H. Rabinowitz
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadison

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