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

Time periodic solutions of nonlinear wave equations

  • Paul H. Rabinowitz


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.


Boundary Condition Wave Equation Periodic Solution Number Theory Algebraic Geometry 
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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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