Abstract
The aim of this paper is to establish the existence of anti-periodic solutions to the following nonlinear anti-periodic problem: a.e. , , in where denotes the extremal point set of the multifunction , and is a nonlinear map from to . Sufficient conditions for the existence of extremal solutions are presented. Also, we prove that the extremal point set of this problem is compact in and dense in the solution set of nonlinear evolution problems with a convex valued perturbation which is multivalued. We apply our results on the control system with a priori feedback.
Highlights
In this paper, we consider the following anti-periodic problems:x + A(t, x) ∈ Ext F(t, x) a.e. t ∈ I, ( )x(T) = –x( ), in RN where I = [, T], F(t, x) : I × RN → RN satisfies some conditions mentioned later, A(t, x) is a nonlinear map from I × RN to RN
The study of anti-periodic solutions for nonlinear evolution equations was initiated by Okochi [ ]
Many authors devoted themselves to the investigation of the existence of anti-periodic solutions to nonlinear evolution equations in Hilbert spaces
Summary
We consider the following anti-periodic problems:. x(T) = –x( ), in RN where I = [ , T], F(t, x) : I × RN → RN satisfies some conditions mentioned later, A(t, x) is a nonlinear map from I × RN to RN. Many authors devoted themselves to the investigation of the existence of anti-periodic solutions to nonlinear evolution equations in Hilbert spaces. Q Liu [ ], ZH Liu [ ] and Wang [ ] considered anti-periodic problem of nonlinear evolution equation in a real reflexive Banach space and obtained some. Inspired by [ ], which considers the problem in Banach space, we continue to consider the existence of solutions for a nonlinear evolution inclusion in RN by relaxing the constraint conditions. Our approach will be based on techniques and results of the theory of the extremal continuous selection theorem and the Schauder fixed point theorem. In Section , we present some basic assumptions and main results, the proofs of the main results are given based on the Schauder fixed point theorem and the extremal continuous selection theorem.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
