RMC - Vol. 7, Num. 2 - R. Cascaval/I. I. Vrabie

Full paper in PDF:
$%R. Caşcaval and I. I. Vrabie, Existence of periodic solutions for a class of nonlinear evolution equations, Rev. Mat. Univ. Complut. Madrid 7 (1994), no. 2, 325–338.%$

Existence of Periodic Solutions for a Class of Nonlinear Evolution Equations

Radu CaŞcaVAL and Ioan I. VRABIE

Dept. of Mathematics
University “Al. J. Cuza” or Iasi
Iasi 6600 — Romania

Received: May 28, 1993

ABSTRACT

In the present paper we prove an existence result concerning $T$ -periodic solutions to a class of nonlinear evolution equations of the form

u'(t)+ Au(t) -) f(t,u(t)), t (- R,

where $A$ is a $m$ -accretive operator acting in a real Hilbert space $H$ and such that $-A$ is the generator of a compact semigroup, while $----- f :R× D(A) --> H$ is continuous and $T$ -periodic with respect to the first argument.

1991 Mathematics Subject Classification: 34C25, 34G20, 35K55.