# Accession Number:

## ADA046435

# Title:

## Periodic and Quasiperiodic Solutions of Delta u + Lambda u + 0(u) = 0.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1977-08-01

# Pagination or Media Count:

## 47.0

# Abstract:

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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics