Third-order boundary value problems with sign-changing solutions

Hopkins, Britney; Kosmatov, Nickolai

doi:10.1016/j.na.2006.05.003

Cited by 40 publications

(24 citation statements)

References 9 publications

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“…However, Al-Smadi et al (2014) have developed an iterative method for handling system of first-order PBVPs based on the RKHM. While Hopkins and Kosmatov (2007) have provided the existence of at least one positive solutions of PBVP in the form u′′′ (x) = f (x, u (x), u′(x), u′′ (x)). Further, Taylors decomposition method for solving linear periodic equation u′′′ (x) = α 1 (x) u′′ (x)+ α 2 (x) u′ (x)+ α 3 (x) u (x)+ α 4 (x) numerically is proposed by Ashyralyev et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

Freihat¹,

Abu-Gdairi²,

Khalil³

et al. 2016

American Journal of Applied Sciences

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Abstract:In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.

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Section: Introductionmentioning

confidence: 99%

Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

Freihat¹,

Abu-Gdairi²,

Khalil³

et al. 2016

American Journal of Applied Sciences

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“…The current analysis of these problems has a great interest and many methods are used to solve such problems. Recently certain three point boundary value problems for nonlinear ordinary differential equations have been studied by many authors [1][2][3][4][5][6][7][8][9]. The literature concerning these problems is extensive and application of theorems of functional analysis has attracted more interest.…”

Section: Introductionmentioning

confidence: 99%

“…The literature concerning these problems is extensive and application of theorems of functional analysis has attracted more interest. Recently, the study of existence of positive solution to third-order boundary value problems has gained much attention and is a rapidly growing field see [1,2,6,[8][9][10][11]. However the approaches used in the literature are usually topological degree theory and fixed-point theorems in cone.…”

Section: Introductionmentioning

confidence: 99%

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

Guezane-Lakoud¹,

Zenkoufi²

2012

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“…In addition, solutions u of (P ), (BC i ) (i = 1, 2, 3, 4) may not be in C 1 (R + ) since w may have zeros in R + . In order to overcome these difficulties, a new Banach space equipped with a weighted norm is introduced, and then we can proceed with the Leray-Schauder continuation principle which was used in many works (see, e.g., [5,7,9,10,11,17]) in order to prove the existence of a solution for the problems (P ), (BC i ) (i = 1, 2, 3, 4).…”

Section: Introductionmentioning

confidence: 99%