Periodic and Quasiperiodic Solutions of Delta u + Lambda u + 0(u) = 0.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In this paper the boundary value problems Delta u lambda ufu, ux, Uy0, u0,yu1,y-0 is studied in the strip 0,1xR, where f is some Csuperscript 2-function which, together with its gradient, vanishes at 0, lambda is a real parameter. It is shown that, for lambda between pi-squared and 4 pi-squared all small solutions are periodic in y. Moreover, singular solutions exist as local Hsuperscript 2-limits of periodic solutions with large periods. For values of lambda beyond 4 pi-squared a formal argument suggests that almost all small solutions are quasiperiodic. The equation is studied as a model for some important but technically cumbersome bifurcation problems in fluid dynamics. Author
- Theoretical Mathematics