Existence of positive solutions for a fourth-order three-point boundary value problem

Guezane-Lakoud, A.; Zenkoufi, L.

doi:10.1007/s12190-014-0863-5

Cited by 7 publications

(4 citation statements)

References 19 publications

(9 reference statements)

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“…Consider, for any 𝑣, 𝑤 ∈ 𝐷 and for 𝑥 ∈ [𝑎, 𝑏], we obtain Using (17), we have 𝛽 < 1 and hence, the operator 𝐹 has fulfilled the condition of Theorem 2.6. This implies that the operator𝐹 has a unique fixed point and is the solution of (1)-(2).…”

Section: Main Results Based On Metricsmentioning

confidence: 99%

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The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions

Madhubabu¹,

Sreedhar

Prasad

2022

J. Adv. App. Comput. Math.

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This research paper aims to establish the uniqueness of the solution to fourth-order nonlinear differential equations v(4)(x) + f (x,v(x)) = 0, x ε [a,b], with non-homogeneous boundary conditions where 0 ≤ a < ζ < b, the constants α, ???? are real numbers and f : [a,b] x R →R is a continuous function with f (x, 0] ≠ 0. Using the sharper bounds on the integral of the kernel, the uniqueness of the solution to the problem is established based on Banach and Rus fixed point theorems on metric spaces. AMS Subject Classification: 34B15, 34B10.

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Section: Main Results Based On Metricsmentioning

confidence: 99%

“…By taking 𝑎 = 0, 𝑏 = 1 in (1) and ( 2), Sun and Zhu [16] established the existence of positive solutions by using Krasnosel'skii fixed point theorem. In the same way, Lakoud and Zenkoufi [17] studied the existence, uniqueness, and positivity of solutions through various fixed-point theorems for 𝜇 = 0.…”

Section: Introductionmentioning

confidence: 97%

The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions

Madhubabu¹,

Sreedhar

Prasad

2022

J. Adv. App. Comput. Math.

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“…The author used Krasnoselskii's fixed point theorem on cone preserving operators for deriving some required criteria. In [13], Guezane-Lakoud et al presented a fourth-order mathematical model of elastic beam in three separate points of domain and studied the existence of positive solutions with the help of fixed point techniques.…”

Section: Introductionmentioning

confidence: 99%

An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

Rezapour

Azzaoui

Tellab

et al. 2021

Journal of Function Spaces

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In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

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“…In 2003, Ma[10] considered the differential equation of fourth order (and establishes the existence of multiple positive solutions. In 2016, Lakoud and Zenkoufi[11] proved the existence results…”

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confidence: 98%

Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems

Sankar¹,

Sreedhar²,

Prasad

2021

Contemporary Mathematics

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The present paper focuses on establishing the existence and uniqueness of solutions to the nonlinear differential equations of order four y(4)(t) + g(t, y(t)) = 0, t ∈ [a, b], together with the non-homogeneous three-point boundary conditions y(a) = 0, y′(a) = 0, y′′(a) = 0, y(b) − αy(ξ ) = λ, where 0 ≤ a < b, ξ ∈ (a, b), α, λ are real numbers and the function g: [a, b] × R→R is a continuous with g(t, 0) ≠ 0. With the aid of an estimate on the integral of kernel, the existence results to the problem are proved by employing fixed point theorem due to Banach.

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Existence of positive solutions for a fourth-order three-point boundary value problem

Abstract: In this paper, we are concerned with a fourth-order three point boundary value problem. We prove the existence, uniqueness and positivity of solutions by using Leray-Schauder nonlinear alternative, Banach contraction theorem and GuoKrasnosel'skii fixed point theorem.

Cited by 7 publications

References 19 publications

The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions

The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions

An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems

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