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On some qualitative properties of mild solutions of nonlocal semilinear functional differential equations

100%

Jain R. S. , Dhakne M. B.

tom Vol. 47, nr 4

854--865

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

On mild solutions of nonlocal second order semilinear functional integro-differential equations

100%

Jain R. S. , Dhakne M. B.

Fasciculi Mathematici

2014

tom Nr 53

65--75

In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of second order nonlocal semilinear functional integro-differential equations of more general type with delay in Banach spaces. Our analysis is based on the theory of strongly continuous cosine family of operators and modified version of Banach contraction theorem.

On existence of mild and classical solutions of second order impulsive implicit differential equations

80%

Jain R. S. , Reddy B. S. , Kadam S. D.

tom Nr 61

71--81

In this paper, we establish the existence and uniqueness results of mild and classical solutions for impulsive implicit second order differential equations with nonlocal condition by using contraction principle. Furthermore, we give an example to illustrate our results.