POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS

Title & Authors
POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Asif, Naseer Ahmad; Eloe, Paul W.; Khan, Rahmat Ali;

Abstract
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\small{\in}$ (0, 1), -y"(t) = g(t, x(t)), t $\small{\in}$ (0, 1), x(0) = y(0) = 0, x(1) = $\small{{\alpha}x(\eta)}$, y(1) = $\small{{\alpha}y(\eta)}$, are obtained. The nonlinearities f, g : (0,1) $\small{\times}$ (0, $\small{\infty}$ ) $\small{\rightarrow}$ (0, $\small{\infty}$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\small{\eta}$, $\small{\alpha}$, satisfy $\small{{\eta}\;{\in}\;}$ (0,1), 0 < $\small{\alpha}$ < $\small{1/{\eta}}$. An example is provided to illustrate the results.
Keywords
positive solutions;singular system of ordinary differential equations;three-point nonlocal boundary value problem;
Language
English
Cited by
1.
Positive solutions to singular system with four-point coupled boundary conditions, Journal of Mathematical Analysis and Applications, 2012, 386, 2, 848
2.
On two systems of non-resonant nonlocal boundary value problems, Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2013, 21, 3
3.
Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations, Mediterranean Journal of Mathematics, 2017, 14, 2
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