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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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| 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 |
| id | doaj-art-8f76b46500e1454cab25a38795a22e4c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| 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 |