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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.

Existence and uniqueness of solution of differential equation of second order in cone metric spaces

Tidke H. L., Dhakne M. B.

Fasciculi Mathematici

2010

Nr 45

121-131

In this paper we investigate the existence and uniqueness for fractional and non-fractional dierential equations in cone metric spaces. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space, fractional calculus and the theory of strongly continuous cosine family.

On differentiability with respect to a parameter of a weak solution of a second order differential equation in Banach space

Jużyniec M.

Czasopismo Techniczne. Nauki Podstawowe

2010

R. 107, z. 1-NP

31-41

The purpose of this paper is to present some theorems on continuity and differentiability with respect to a parameter h of a weak solution of the evolution equation u(t) = A[h]u(t) + f[h](t).

Celem artykułu jest przedstawienie twierdzeń o ciągłej zależności od parametru oraz różniczkowalności względem parametru h słabego rozwiązania ewolucyjnego równania różniczkowego u(t) = A[h]u(t) + f[h](t).