Solvability and asymptotic stability of a nonlinear functional-integral equation

Liu, Zeqing; Kang, Shin Min; Ume, Jeong Sheok

doi:10.1016/j.aml.2011.01.001

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…Some more general equations than (2) were also studied in [11], such as (t) k(t, s)f (s, x(θ (s)))ds Recently, using the technique of the measure of noncompactness and the Darbo fixed point theorem, Z. Liu et al [7] have proved the existence and asymptotic stability of solutions for the equation…”

Section: S)f (S X(θ (S)))ds + σ (T)mentioning

confidence: 99%

Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Ngoc

Long

2015

Acta Math Vietnam

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Section: S)f (S X(θ (S)))ds + σ (T)mentioning

confidence: 99%

Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Ngoc

Long

2015

Acta Math Vietnam

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“…Using the technique of the measure of noncompactness and Darbo's fixed point theorem, Z. Liu et al [12] have proved the existence and asymptotic stability of solutions for the equation…”

Section: Introductionmentioning

confidence: 99%

Solvability, stability, smoothness and compactness of the set of solutions for anonlinear functional integral equation

Thuc¹,

Ngoc²,

Long³

2021

Turk J Math

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This paper is devoted to the study of the following nonlinear functional integral equationwhere τi, σ1, σ2, σ3are the given continuous functions and f : [0, 1] → R is an unknown function. First, two sufficient conditions for the existence and some properties of solutions of Eq. (E) are proved. By using Banach's fixed point theorem, we have the first sufficient condition yielding existence, uniqueness and stability of the solution. By applying Schauder's fixed point theorem, we have the second sufficient condition for the existence and compactness of the solution set. An example is also given in order to illustrate the results obtained here. Next, in the case of Ψ ∈ C 2 ([0, 1] × [0, 1] × RR), we investigate the quadratic convergence for the solution of Eq. (E). Finally, the smoothness of the solution depending on data is established.

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“…The integral equations have been investigated from different mathematical areas of sciences and technology [1][2][3][4][5][6][7][8][9]. For this, many authors have been established different analytic and numeric methods.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic model for solving mixed integral equation in some domains

Abdou

Awad

2020

J Egypt Math Soc

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In this paper, we discuss the solution of mixed integral equation with generalized potential function in position and the kernel of Volterra integral term in time. The solution will be discussed in the space $$L_{2} (\Omega ) \times C[0,T],$$ L 2 ( Ω ) × C [ 0 , T ] , $$0 \le t \le T < 1$$ 0 ≤ t ≤ T < 1 , where $$\Omega$$ Ω is the domain of position and $$t$$ t is the time. The mixed integral equation is established from the axisymmetric problems in the theory of elasticity. Many special cases when kernel takes the potential function, Carleman function, the elliptic function and logarithmic function will be established.

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Solvability and asymptotic stability of a nonlinear functional-integral equation

Cited by 7 publications

References 11 publications

Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Solvability, stability, smoothness and compactness of the set of solutions for anonlinear functional integral equation

An asymptotic model for solving mixed integral equation in some domains

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