Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2009.01.01
  • Published : 2010.09.01
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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

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