Existence theorems for a second order m-point boundary value problem at resonance
Let f:[0,1]×R2→R be function satisfying Caratheodory's conditions and e(t)∈L1[0,1]. Let η∈(0,1), ξi∈(0,1), ai≥0, i=1,2,…,m−2, with ∑i=1m−2ai=1, 0<ξ1<ξ2<…<ξm−2<1 be given. This paper is concerned with the problem of existence of a solution for the following boundary value problems...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000901 |
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| _version_ | 1832565666098446336 |
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| author | Chaitan P. Gupta |
| author_facet | Chaitan P. Gupta |
| author_sort | Chaitan P. Gupta |
| collection | DOAJ |
| description | Let f:[0,1]×R2→R be function satisfying Caratheodory's conditions and e(t)∈L1[0,1]. Let η∈(0,1), ξi∈(0,1), ai≥0, i=1,2,…,m−2, with ∑i=1m−2ai=1, 0<ξ1<ξ2<…<ξm−2<1 be given. This paper is concerned with the problem of existence of a solution
for the following boundary value problems
x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=x(η),x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=∑i=1m−2aix(ξi). |
| format | Article |
| id | doaj-art-aaa1a71419294989925e75980728287a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aaa1a71419294989925e75980728287a2025-02-03T01:07:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118470571010.1155/S0161171295000901Existence theorems for a second order m-point boundary value problem at resonanceChaitan P. Gupta0Department of Mathematics, University of Nevada, Reno, NV 89557, USALet f:[0,1]×R2→R be function satisfying Caratheodory's conditions and e(t)∈L1[0,1]. Let η∈(0,1), ξi∈(0,1), ai≥0, i=1,2,…,m−2, with ∑i=1m−2ai=1, 0<ξ1<ξ2<…<ξm−2<1 be given. This paper is concerned with the problem of existence of a solution for the following boundary value problems x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=x(η),x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=∑i=1m−2aix(ξi).http://dx.doi.org/10.1155/S0161171295000901 |
| spellingShingle | Chaitan P. Gupta Existence theorems for a second order m-point boundary value problem at resonance International Journal of Mathematics and Mathematical Sciences |
| title | Existence theorems for a second order m-point boundary value problem at resonance |
| title_full | Existence theorems for a second order m-point boundary value problem at resonance |
| title_fullStr | Existence theorems for a second order m-point boundary value problem at resonance |
| title_full_unstemmed | Existence theorems for a second order m-point boundary value problem at resonance |
| title_short | Existence theorems for a second order m-point boundary value problem at resonance |
| title_sort | existence theorems for a second order m point boundary value problem at resonance |
| url | http://dx.doi.org/10.1155/S0161171295000901 |
| work_keys_str_mv | AT chaitanpgupta existencetheoremsforasecondordermpointboundaryvalueproblematresonance |