Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1215.34069
Chen, Yuqing; Nieto, Juan J.; O'Regan, Donal
Anti-periodic solutions for evolution equations associated with maximal monotone mappings.
(English)
[J] Appl. Math. Lett. 24, No. 3, 302-307 (2011). ISSN 0893-9659

The authors consider the existence of anti-periodic solutions for differential inclusions in a real Hilbert space $H$. The first result concerns the problem $$x^{\prime }(t)\in -Ax(t)+f(t)\text{ a.e. on }\Bbb{R},$$ $$x(t)=-x(t+T)\text{ for }t\in \Bbb{R}.$$ $A$ is assumed to be an odd maximal monotone mapping, $D(A)$ is symmetric and convex, $f$ is $L^{2}$ and satisfies $f(t)=-f(t+T)$ for $t\in \Bbb{R}$, $\|g\| \leq M\| x\|$ for all $x\in D(A)$ and $g\in Ax$, and $M>0$ is a constant such that $MT<2$. The other theorem concerns the problem $$x^{\prime }(t)\in -Ax(t)+\partial G(x(t))+f(t)\text{ a.e. on }\Bbb{R},$$ $$x(t)=-x(t+T)\text{ for }t\in \Bbb{R}.$$ In addition to the hypotheses of the first result, it is assumed that $G$ is continuously differentiable and even, $\partial G$ maps bounded sets to bounded sets, and $D(A)$ is compactly embedded in $H$. In the case in which $A$ is the subdifferential of a lower semi-continuous convex function, the authors obtained similar results as in [{\it Y. Q. Chen, D. O'Regan} and {\it J. J. Nieto}, Math. Comput. Modelling 46, No.~9--10, 1183--1190 (2007; Zbl 1142.34313)]. The authors conclude the paper by applying the first of these theorems to a boundary value problem for a partial differential equation.
[Daniel C. Biles (Nashville)]
MSC 2000:
*34G25 Evolution inclusions
34C25 Periodic solutions of ODE

Keywords: evolution inclusion; maximal monotone; anti-periodic solution; existence of solutions; differential inclusion

Citations: Zbl 1142.34313

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences