Coupled System of Boundary Value Problems

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: National University of Singapore, Department of Mathematics
Donal O’Regan: National University of Ireland, Department of Mathematics
Patricia J. Y. Wong: Nanyang Technological University, Division of Mathematics

Chapter Chapter 11 in Positive Solutions of Differential, Difference and Integral Equations, 1999, pp 119-130 from Springer

Abstract: Abstract In this chapter we shall investigate the existence of positive solutions of the coupled system of boundary value problem 11.1 $$u'' + f(t,\nu ) = 0$$ 11.1 $$\nu '' + g(t,u) = 0$$ 11.2 $$\left\{ {\begin{array}{*{20}{c}}{{\alpha _1}u(0) - {\beta _1}u''(0) = 0} \\{{\gamma _1}u(1) + {\delta _1}u''(1) = 0}\end{array}} \right.$$ 11.2 $$\left\{ {\begin{array}{*{20}{c}}{{\alpha _2}\nu (0) - {\beta _2}\nu ''(0) = 0} \\{{\gamma _2}\nu (1) + {\delta _2}\nu ''(1) = 0}\end{array}} \right.$$ where α i ≥ 0, β i ≥ 0, γ i ≥ 0, δ i ≥ 0, ρ i = γ i β i +α i γ i +α i δ i > 0, i = 1, 2.

Keywords: Ordinary Differential Equation; Point Theorem; Couple System; Existence Result; General Existence (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9171-3_11

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DOI: 10.1007/978-94-015-9171-3_11

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