Abstract
The aim of the present paper is to study the global existence of solutions of nonlinear second order integrodifferential equation in Banach space. Our analysis is based on an application of the Leray‐Schauder alternative and rely on a priori bounds of solutions.
Highlights
Let X be a Banach space with norm
Let B = C([0, T ], X) be the Banach space of all continuous functions from [0, T ] into X endowed with supremum norm x B = sup { x(t) : t ∈ [0, T ]}
The purpose of this paper is to prove the global existence of solutions of the following initial value problem for second order integrodifferentioal equations of the form t
Summary
Let X be a Banach space with norm. Let B = C([0, T ], X) be the Banach space of all continuous functions from [0, T ] into X endowed with supremum norm x B = sup { x(t) : t ∈ [0, T ]}. The purpose of this paper is to prove the global existence of solutions of the following initial value problem for second order integrodifferentioal equations of the form t (1.1) (r(t)x (t)) = f t, x(t), k(t, s)g(s, x(s))ds , t ∈ [0, T ]. The main purpose of this paper is to study the global existence of solutions of initial value problem (1.1)-(1.2) by using an application of the topological transversality theorem known as Leray-Schauder alternative.
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