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1
Content available remote On nonlinear second order Volterra-Fredholm functional integrodifferential equation with nonlocal condition in Banach spaces
Dhakne M. B., Bora P. S.
Fasciculi Mathematici
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2015
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Nr 54
75--96
EN
Our purpose in this paper is to study the existence of solution of nonlinear second order mixed functional integrodierential equation with nonlocal condition in Banach space by employing two different techniques namely the Darbo-Sadovskii's fixed point theorem with Hausdorff's measure of noncompactness and the Leray Schauder Alternative
2
Content available remote On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition
Jain R. S., Dhakne M. B.
Demonstratio Mathematica
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2015
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Vol. 48, nr 3
413--423
EN
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.
3
Content available remote On mild solutions of nonlocal second order semilinear functional integro-differential equations
Jain R. S., Dhakne M. B.
Fasciculi Mathematici
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2014
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Nr 53
65--75
EN
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.
4
Content available remote On some qualitative properties of mild solutions of nonlocal semilinear functional differential equations
Jain R. S., Dhakne M. B.
Demonstratio Mathematica
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2014
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Vol. 47, nr 4
854--865
EN
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.
5
Content available remote Global existence for abstract nonlinear Volterra-Fredholm functional integrodifferential equation
Dhakne M. B., Kucche K. D.
Demonstratio Mathematica
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2012
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Vol. 45, nr 1
117-127
EN
In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of solution.
6
Content available remote Existence and uniqueness of solution of differential equation of second order in cone metric spaces
Tidke H. L., Dhakne M. B.
Fasciculi Mathematici
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2010
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Nr 45
121-131
EN
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.
7
Content available remote Existence and uniqueness of mild and strong solutions of nonlinear Volterra integrodifferential equations in Banach spaces
Tidke H. L., Dhakne M. B.
Demonstratio Mathematica
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2010
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Vol. 43, nr 3
643-652
EN
In this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.
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