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.

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 of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyong Qin ◽  
Zhenyun Gu ◽  
Youliang Fu ◽  
Tongxing Li
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Control Function ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Continuous Control ◽  
Nonlocal Problems ◽  
Piecewise Continuous ◽  
Fixed Point Methods

This paper is concerned with the existence results of nonlocal problems for a class of fractional impulsive integrodifferential equations in Banach spaces. We define a piecewise continuous control function to obtain the results on controllability of the corresponding fractional impulsive integrodifferential control systems. The results are obtained by means of fixed point methods. An example to illustrate the applications of our main results is given.

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 Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 113-126
Author(s):  
Xuping Zhang ◽  
Qiyu Chen ◽  
Yongxiang Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Linear Part ◽  
Fractional Power ◽  
Interpolation Spaces ◽  
Partial Differential ◽  
Nonlocal Initial Conditions ◽  
Spatial Derivatives

AbstractThis paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.

scholarly journals The Kneser property for abstract retarded functional differential equations with infinite delay

2003 ◽  
Vol 2003 (26) ◽  
pp. 1645-1661 ◽  
Author(s):  
Hernán R. Henríquez
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
First Order ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

We establish existence of mild solutions for a class of semilinear first-order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.

On the existence of mild solutions for a class of fractional differential equations with nonlocal conditions in the α-norm

2014 ◽  
Vol 51 (2) ◽  
pp. 141-154
Author(s):  
Mohamed Abbas
Keyword(s):  
Cauchy Problem ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Nonlinear Part ◽  
Fractional Differential ◽  
Fractional Cauchy Problem ◽  
Lipschitz Conditions

This paper concerns the existence of mild solutions for some fractional Cauchy problem with nonlocal conditions in the α-norm. The linear part of the equations is assumed to generate an analytic compact bounded semigroup, and the nonlinear part satisfies some Lipschitz conditions with respect to the fractional power norm of the linear part. By using a fixed point theorem of Sadovskii, we establish some existence results which generalize ones in the case of fractional order derivative.

scholarly journals Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Cellular Neural Network ◽  
Continuous Functions ◽  
Practical Stability ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential ◽  
Control Functional

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

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