On the existence of solutions of Volterra integral equations in a generalized interpretation with a continuous kernel

Guryanova I.E.

Financial University under the Government of the Russian Federation 125993, Moscow, Leningradskiy Ave., 49

The nonlinear Volterra integral equations are considered in a generalized interpretation on compact sets M(t). of the form

x(t)=f(t)+∫_M(t)^ ▒〖K(t,s,x(s))dμ_s 〗, (1)

The mapping M: М:   2satisfies the axiom system. For equation (1) in [1 – 2] the existence, uniqueness and stability theorems of solutions are obtained. The paper considers equation (1) with a continuous kernel that does not satisfy the Lipschitz condition. Using Schauder's principle and Krasnoselsky's theorem, the existence theorems of a solution for integral equation (1) are proved.


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