On an abstract nonlinear functional second order Volterra integrodifferential equation

Pramod M Dhakane

Abstract


In this paper, we prove the existence, uniqueness and boundedness of solutions of a nonlinear functional second order Volterra integrodifferential equation in a general Banach space. The theory of strongly continuous cosine family, modified version of Banach contraction mapping principle and Pachpatte’s integral inequality are main techniques employed in our analysis

Keywords


Volterra integro-differential equations; Cosine family; Modified version of Banach contraction mapping principle; Pachpatte's integral inequality

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References


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DOI: http://dx.doi.org/10.23755/rm.v51i0.1252

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