Abstract
In this work we present some new results concerning the existence of solutions for first-order nonlinear integro-differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and classical fixed-point theorems. MR(2000)Subject Classification. 34D09,34D99.
Highlights
Introduction and preliminariesAs is known, integro-differential equations find many applications in various mathematical problems, see Cordunean’s book [1], Guo et al.’s book [2] and references therein for details
This paper mainly considers the existence of solutions for the following first-order nonlinear integro-differential system with periodic boundary value conditions
Existence results for periodic conditions To begin with, we consider the following periodic boundary value problem x + m(t)x = g(t, x, (Kx)(t)), t ∈ [0, 1]; (2:1)
Summary
Introduction and preliminariesAs is known, integro-differential equations find many applications in various mathematical problems, see Cordunean’s book [1], Guo et al.’s book [2] and references therein for details. This paper mainly considers the existence of solutions for the following first-order nonlinear integro-differential system with periodic boundary value conditions. 2. Existence results for periodic conditions To begin with, we consider the following periodic boundary value problem x + m(t)x = g(t, x, (Kx)(t)), t ∈ [0, 1]; (2:1)
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