## Abstract and Applied Analysis

### Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems

#### Abstract

In the case of $K \neq \overline{D(A)}$, we study Cauchy problems and periodic problems for nonlinear evolution equation $u(t) \in K$, $u'(t)+Au(t)\ni f(t,u(t))$, $0 \leq t \leq T$, where $A$ is a maximal monotone operator on a Hilbert space $H$, $K$ is a closed, convex subset of $H$, $V$ is a subspace of $H$, and $f: [0,T] \times (K \cap V) \rightarrow H$ is of Carathéodory type.

#### Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 3 (2004), 183-203.

Dates
First available in Project Euclid: 4 May 2004

https://projecteuclid.org/euclid.aaa/1083679146

Digital Object Identifier
doi:10.1155/S1085337504311073

Mathematical Reviews number (MathSciNet)
MR2058501

Zentralblatt MATH identifier
1082.47045

Subjects
Primary: 47H06: Accretive operators, dissipative operators, etc. 47H20
Secondary: 35B10

#### Citation

Hirano, Norimichi; Shioji, Naoki. Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems. Abstr. Appl. Anal. 2004 (2004), no. 3, 183--203. doi:10.1155/S1085337504311073. https://projecteuclid.org/euclid.aaa/1083679146