Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions | Zendy

Mısır J. Mardanov | Zendy; Rəşad Sirac Mammadov | Zendy; Sahib Gasimov | Zendy; Ya. A. Sharifov | Zendy

Open Access

Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions

Author(s) -

Mısır J. Mardanov,

Rəşad Sirac Mammadov,

Sahib Gasimov,

Ya. A. Sharifov

Publication year - 2021

Publication title -

bulletin of the karaganda university-mathematics

Language(s) - English

Resource type - Journals

eISSN - 2663-5011

pISSN - 2518-7929

DOI - 10.31489/2021m2/74-83

Subject(s) - uniqueness , mathematics , fixed point theorem , contraction mapping , mathematical analysis , boundary value problem , picard–lindelöf theorem , nonlinear system , contraction principle , differential equation , banach fixed point theorem , order (exchange) , fixed point , physics , quantum mechanics , finance , economics

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

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