Positive solutions to singular system with four-point coupled boundary conditions

By N. Asif, Rahmat Ali Khan. 2012

52 citations recorded by the source corpus.

Abstract Existence of positive solution to a nonlinear singular system with four-point coupled boundary conditions of the type − x ″ ( t ) = f ( t , x ( t ) , y ( t ) ) , t ∈ ( 0 , 1 ) , − y ″ ( t ) = g ( t , x ( t ) , y ( t ) ) , t ∈ ( 0 , 1 ) , x ( 0 ) = 0 , x ( 1 ) = α y ( ξ ) , y ( 0 ) = 0 , y ( 1 ) = β x ( η ) , is established. The nonlinearities f , g : ( 0 , 1 ) × [ 0 , ∞ ) × [ 0 , ∞ ) → [ 0 , ∞ ) are continuous and singular at t = 0 , t = 1 , while the parameters α, β, ξ, η satisfy ξ , η ∈ ( 0 , 1 ) , 0 α β ξ η 1 . An example is included to show the applicability of our result.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/481649b0c7628035ffd33be5180278c2edfd8799

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In Numerical Analysis

Citations in the corpus

Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions (2013, background): “In particular we are interested in systems that present a coupling in the boundary conditions (BCs); this type of problems have been studied in [5, 6, 7, 10, 11, 32, 36, 47] and often occur in applications, for example when modelling the displacement of a suspension bridge subject to nonlinear contr”
Non-negative solutions of systems of ODEs with coupled boundary conditions (2012, unknown): “A recent paper in this line of research is the one by Asif and Khan [8], who study the four-point coupled system u00ðtÞ þ f1ðt;uðtÞ;vðtÞÞ ¼ 0; t 2 ð0;1Þ; v 00ðtÞ þ f2ðt;uðtÞ; vðtÞÞ ¼ 0; t 2 ð0;1Þ; uð0Þ ¼ 0; uð1Þ ¼ d12vðg12Þ; vð0Þ ¼ 0; vð1Þ ¼ d22uðg22Þ: ð1Þ The authors prove, via the well-known Guo–K”