Multiple Positive Solutions of a Second Order Nonlinear Semipositone m‐Point Boundary Value Problem on Time Scales

Chengjun Yuan and Yongming Liu

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: In this paper, we study a general second‐order m‐point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t) + a(t)uΔ(t) + b(t)u(t) + λq(t)f(t, u(t)) = 0, t ∈ (0,1) 𝕋, u(ρ(0)) = 0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed‐point theorems in a cone.

Date: 2010
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https://doi.org/10.1155/2010/261741

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:261741

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