Periodic solution of nonlinear parabolic equations

1 January 1979

journal article
research article
Published by Taylor & Francis in Communications in Partial Differential Equations

Vol. 4 (12) , 1299-1387
https://doi.org/10.1080/03605307908820129

Abstract

The paper deals with global bifurcation from an equilibrium of periodic orbits for abstract nonlinear autonomous evolution equations: If the linearized problem has an odd number of exchanges of stability, then there is a continuum of starting points, parameters and periods, which is either unbounded or connects the equilibrium point to an odd number of stationary points with an odd number of exchanges of stability. Applications are given to quasilinear parabolic equations, in particular to the Navier-Stokes equations.

Keywords

EQUILIBRIUM POINT

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