Positive Solutions to Nonlinear First-Order Nonlocal BVPs with Parameter on Time Scales
We discuss the existence of solutions for the first-order multipoint BVPs on time scale 𝕋: uΔ(t)+p(t)u(σ(t))=λf(t,u(σ(t))), t∈[0,T]𝕋, u(0)-∑i=1mαiu(ξi)=0, where λ&#...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2011/198598 |
| Summary: | We discuss the existence of solutions for the first-order multipoint BVPs on time scale 𝕋: uΔ(t)+p(t)u(σ(t))=λf(t,u(σ(t))), t∈[0,T]𝕋, u(0)-∑i=1mαiu(ξi)=0, where λ>0 is a parameter, T>0 is a fixed number, 0,T∈𝕋, f:[0,T]𝕋×[0,∞)→[0,∞) is continuous, p is regressive and rd-continuous, αi≥0, ξi∈𝕋, i=1,2,…,m, 0=ξ0<ξ1<ξ2<⋯<ξm-1<ξm=σ(T), and 1-∑i=1m(αi/ep(ξi,0))>0. For suitable λ>0, some existence, multiplicity, and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index. |
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| ISSN: | 1687-2762 1687-2770 |