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Open Access Research

Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions

Jingrui Zhang1*, Yi Cheng23, Changqin Yuan2 and Fuzhong Cong2

Author Affiliations

1 School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

2 Fundamental Department, Aviation University of Air Force, Changchun, 130022, People’s Republic of China

3 Institute of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

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Boundary Value Problems 2013, 2013:15  doi:10.1186/1687-2770-2013-15

Published: 5 February 2013

Abstract

In this paper, we consider the nonlocal problems for nonlinear first-order evolution inclusions in an evolution triple of spaces. Using techniques from multivalued analysis and fixed point theorems, we prove existence theorems of solutions for the cases of a convex and of a nonconvex valued perturbation term with nonlocal conditions. Also, we prove the existence of extremal solutions and a strong relaxation theorem. Some examples are presented to illustrate the results.

MSC: 34B15, 34B16, 37J40.

Keywords:
evolution inclusions; nonlocal conditions; Leray-Schauder alternative theorem; extremal solutions