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Existence and uniqueness of solutions of certain second order nonlinear equations


Abstract


The existence, uniqueness and other properties of solutions of nonlinear second order Volterra integrodifferential equation in a general Banach space are studied. The main tools in our analysis is based on the theory of the strongly continuous cosine family, a modified version of contraction mapping principle and the integral inequality established by B. G. Pachpatte.

DOI Code: 10.1285/i15900932v30n2p73

Keywords: Volterra integrodifferential equation; uniqueness; continuous dependence; cosineand sine family; integral inequality

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