Optimal Mild Solutions for a Class of Nonlocal Multi-Valued Stochastic Delay Differential Equations

Zuomao Yan () and Li Han ()
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Zuomao Yan: Hexi University
Li Han: Hexi University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 17, 1053-1075

Abstract: Abstract In this paper, we introduce a new class of impulsive multi-valued stochastic delay differential equations with nonlocal conditions in separable Hilbert spaces. Using stochastic analysis, analytic semigroup, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of optimal mild solutions for these systems in the $$\alpha $$ α -norm. An example is provided to illustrate the applicability of our results.

Keywords: Impulsive multi-valued stochastic delay differential equations; Optimal mild solutions; Fractional powers of closed operators; Nonlocal conditions; Fixed point theorem; 34A37; 34A60; 35R60; 60H15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01490-2

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