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http://dx.doi.org/10.4134/JKMS.2010.47.5.985

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

Asif, Naseer Ahmad (CENTRE FOR ADVANCED MATHEMATICS AND PHYSICS NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY CAMPUS OF COLLEGE OF ELECTRICAL AND MECHANICAL ENGINEERING PESHAWAR ROAD)
Eloe, Paul W. (DEPARTMENT OF MATHEMATICS UNIVERSITY OF DAYTON)
Khan, Rahmat Ali (CENTRE FOR ADVANCED MATHEMATICS AND PHYSICS NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY CAMPUS OF COLLEGE OF ELECTRICAL AND MECHANICAL ENGINEERING PESHAWAR ROAD, DEPARTMENT OF MATHEMATICS UNIVERSITY OF DAYTON)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.5, 2010 , pp. 985-1000 More about this Journal
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 $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.
Keywords
positive solutions; singular system of ordinary differential equations; three-point nonlocal boundary value problem;
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