Nontrivial Solution of a Nonlinear Sixth-Order Boundary Value
                        Problem

Bekri, Zouaoui; Benaicha, Slimane

doi:10.1515/wwfaa-2018-0002

Cited by 5 publications

(2 citation statements)

References 1 publication

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“…We shall make use of the following theorem of (Bekri & Benaicha, 2018) and (Shanmugam et al, 2019), the Leray-Schauder form of the fixed point theorem appears in (Isac, 2006), (Deimling, 1985) and (Zvyagin & Baranovskii, 2010):…”

Section: Solutionmentioning

confidence: 99%

Existence of a solution for a general order boundary value problem using the Leray-Schauder fixed point theorem

Fabiano¹,

Parvaneh²

2021

Vojnotehnički glasnik

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Introduction/purpose: This paper illustrates the existence of a generic Green's function for a boundary value problem of arbitrary order that appears in many phenomena of heat convection, e.g. in the atmosphere, in the oceans, and on the Sun's surface. Methods: A fixed point theorem in the Leray-Schauder form has been used to establish the existence of a fixed point in the problem. Results: The existence of a solution has been shown for an arbitrary order of the problem. Some practical examples are proposed. Conclusions: The boundary problem has a solution for an arbitrary order n.

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Section: Solutionmentioning

confidence: 99%

Existence of a solution for a general order boundary value problem using the Leray-Schauder fixed point theorem

Fabiano¹,

Parvaneh²

2021

Vojnotehnički glasnik

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“…Todorčević [20] presented harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. Recently Zouaoui Bekri [21] studied sixth-order nonlinear boundary value problem using the Leray-Schauder alternative theorem. Ma [22] has given the existence and uniqueness theorems based on the Leray-Schauder fixed point theorem for some fourth-order nonlinear boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Shanmugam

Muthiah

Radenović

2019

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Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions

Haddouchi,

Houari

2024

Math Methods in App Sciences

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This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.

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Nontrivial Solution of a Nonlinear Sixth-Order Boundary Value Problem

Cited by 5 publications

References 1 publication

Existence of a solution for a general order boundary value problem using the Leray-Schauder fixed point theorem

Existence of a solution for a general order boundary value problem using the Leray-Schauder fixed point theorem

Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions

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