Multiple positive solutions for nonlinear dynamical systems on a measure chain

In this paper, we consider the following dynamical system on a measure chain: u 1 ΔΔ(t)+f 1(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], u 2 ΔΔ(t)+f 2(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], with the Sturm–Liouville boundary value conditions αu i(a)−βu i Δ(a)=0, γu i(σ(b))+δu i Δ(σ(b))=0 for i=1,2. Some results ar...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2004-01, Vol.162 (2), p.421-430
Main Authors: Li, Wan-Tong, Sun, Hong-Rui
Format: Article
Language:English
Subjects:
Cone
Exact sciences and technology
Finite differences and functional equations
Fixed point
Mathematical analysis
Mathematics
Measure chain
Ordinary differential equations
Positive solution
Sciences and techniques of general use
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Summary:In this paper, we consider the following dynamical system on a measure chain: u 1 ΔΔ(t)+f 1(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], u 2 ΔΔ(t)+f 2(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], with the Sturm–Liouville boundary value conditions αu i(a)−βu i Δ(a)=0, γu i(σ(b))+δu i Δ(σ(b))=0 for i=1,2. Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2003.08.032