Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives

Chen, Huiling; Cui, Yujun

doi:10.1186/s13660-022-02907-9

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…While Kasi Viswanadham et al, (2010) proposed Galerkin method with quintic B-splines as basis functions to find the numerical solution of fourth order boundary value problems. Chen and Cui (2023) studied the existence and uniqueness of solution for fully fourth-order differential equations. The proof will rely on Perov's fixed point theorem in complete generalized metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Eleventh Degree Polynomial Series Solution Approach of Special Non-linear Fourth Order Boundary Value Problems

Mutawakilu,

Bello

2024

USci

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In this paper a new eleventh degree polynomial series solution approach is developed for the solution of special non-linear fourth order boundary value problems. The method consist first of obtaining a linear differentials system of twelve equations from the boundary conditions, governing equation and its three successive derivatives which were evaluated at boundary points. Secondly we assume the approximate solution in the form of a polynomial of degree eleventh with twelve unknown coefficients. To determine the unknown coefficients we incorporate the assumed solution into linear differentials systems of twelve equations which results into a linear systems of twelve equations with twelve unknown and which can be solve uniquely. It is clear from the tables and figures that the method is in good agreement with the exact and with some existing results in the literatures. Also it can be seen from example 3.3 that the exact solution is reproduced which is an added advantage of the method.

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Section: Introductionmentioning

confidence: 99%

Eleventh Degree Polynomial Series Solution Approach of Special Non-linear Fourth Order Boundary Value Problems

Mutawakilu,

Bello

2024

USci

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Existence of Nontrivial Solutions for Boundary Value Problems of Fourth-Order Differential Equations

2024

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This article investigates the solvability problem of fourth-order differential equations with two-point boundary conditions; specifically, conclusions regarding sign-changing solutions are obtained. The methods used in this article are fixed-point theorems on lattices. Firstly, under some sublinear conditions, the existence of three nontrivial solutions is demonstrated, including a sign-changing solution, a negative solution and a positive solution. Secondly, under some unilaterally asymptotically linear and superlinear conditions, the existence of at least one sign-changing solution is proved. Finally, this article provides several specific examples to illustrate the obtained conclusions.

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Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives

Cited by 2 publications

References 28 publications

Eleventh Degree Polynomial Series Solution Approach of Special Non-linear Fourth Order Boundary Value Problems

Eleventh Degree Polynomial Series Solution Approach of Special Non-linear Fourth Order Boundary Value Problems

Existence of Nontrivial Solutions for Boundary Value Problems of Fourth-Order Differential Equations

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