Nonresonance conditions for fourth order nonlinear boundary value problems

This paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. We obta...

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Main Authors: C. De Coster, C. Fabry, F. Munyamarere
Format: Article
Language:English
Published: Wiley 1994-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171294001031
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author C. De Coster
C. Fabry
F. Munyamarere
author_facet C. De Coster
C. Fabry
F. Munyamarere
author_sort C. De Coster
collection DOAJ
description This paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. We obtain existence conditions related to uniqueness conditions for the solution of the linear problemu(4)=au+bu″,u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).
format Article
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institution Kabale University
issn 0161-1712
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language English
publishDate 1994-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-8f76b46500e1454cab25a38795a22e4c2025-02-03T01:02:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117472574010.1155/S0161171294001031Nonresonance conditions for fourth order nonlinear boundary value problemsC. De Coster0C. Fabry1F. Munyamarere2Département de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve B-1348, BelgiumDépartement de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve B-1348, BelgiumDépartement de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve B-1348, BelgiumThis paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. We obtain existence conditions related to uniqueness conditions for the solution of the linear problemu(4)=au+bu″,u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).http://dx.doi.org/10.1155/S0161171294001031nonresonance conditionsfourth order periodic BVPeigenlines.
spellingShingle C. De Coster
C. Fabry
F. Munyamarere
Nonresonance conditions for fourth order nonlinear boundary value problems
International Journal of Mathematics and Mathematical Sciences
nonresonance conditions
fourth order periodic BVP
eigenlines.
title Nonresonance conditions for fourth order nonlinear boundary value problems
title_full Nonresonance conditions for fourth order nonlinear boundary value problems
title_fullStr Nonresonance conditions for fourth order nonlinear boundary value problems
title_full_unstemmed Nonresonance conditions for fourth order nonlinear boundary value problems
title_short Nonresonance conditions for fourth order nonlinear boundary value problems
title_sort nonresonance conditions for fourth order nonlinear boundary value problems
topic nonresonance conditions
fourth order periodic BVP
eigenlines.
url http://dx.doi.org/10.1155/S0161171294001031
work_keys_str_mv AT cdecoster nonresonanceconditionsforfourthordernonlinearboundaryvalueproblems
AT cfabry nonresonanceconditionsforfourthordernonlinearboundaryvalueproblems
AT fmunyamarere nonresonanceconditionsforfourthordernonlinearboundaryvalueproblems