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

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

Fasciculi Mathematici

2018

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.

On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

2015

Vol. 48, nr 3

413--423

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

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

Jain R. S., Dhakne M. B.

Fasciculi Mathematici

2014

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

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

2014

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.