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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |