Mild solutions of evolution quantum stochastic differential equations with nonlocal conditions

2020 ◽  
Vol 43 (10) ◽  
pp. 6254-6261
Author(s):  
Sheila A. Bishop ◽  
Godwin A. Okeke ◽  
Kanayo Eke
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals On a Coupled System of Stochastic Ito^-Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2571
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Integral ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Nonlocal Problems ◽  
Integral Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Random Integral

The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination between the three senses of derivatives, the stochastic Ito^-differential and the fractional and integer orders derivative for the second order stochastic process in two nonlocal problems of a coupled system of two random and stochastic differential equations with two nonlocal stochastic and random integral conditions and a coupled system of two stochastic and random integral conditions. We study the existence of mean square continuous solutions of these two nonlocal problems by using the Schauder fixed point theorem. We discuss the sufficient conditions and the continuous dependence for the unique solution.

Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Leszek Olszowy
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Continuous Functions ◽  
Evolution System ◽  
Impulsive Conditions ◽  
Measures Of Noncompactness ◽  
Piecewise Continuous ◽  
Unbounded Intervals

AbstractThis paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.

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