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Yan, Zuomao; Han, Li

Optimal mild solutions for a class of nonlocal multi-valued stochastic delay differential equations. (English) Zbl 1416.34063

J. Optim. Theory Appl. 181, No. 3, 1053-1075 (2019).
Summary: 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 \(\alpha\)-norm. An example is provided to illustrate the applicability of our results.

Cited in 3 Documents

MSC:

34K50 Stochastic functional-differential equations
34K30 Functional-differential equations in abstract spaces
34A45 Theoretical approximation of solutions to ordinary differential equations
34K09 Functional-differential inclusions
47N20 Applications of operator theory to differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

impulsive multi-valued stochastic delay differential equations; optimal mild solutions; fractional powers of closed operators; nonlocal conditions; fixed point theorem
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References:

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