Existence of Solutions for a Class of Nonlinear Evolution Inclusions with Nonlocal Conditions

Yi Cheng ()
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Yi Cheng: Bohai University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 1, No 2, 13-33

Abstract: Abstract This paper deals with the nonlocal problems for a class of nonlinear first-order evolution inclusions. Some existence results are established for the cases of a convex and of a nonconvex valued perturbation terms. Also, the existence of extremal solutions and a strong relaxation theorem are obtained. Subsequently a nonlinear hyperbolic optimal control problem is considered and the existence theorems based on the proven results are obtained. Then the nonlinear version of “bang–bang” principle for control systems is given as well by utilizing the relaxation theorem.

Keywords: Evolution inclusions; Nonlocal conditions; Pseudomonotone operator; Extremal solutions (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0446-x

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