대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권5호
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  • Pages.985-1000
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  • 2010
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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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)
  • 투고 : 2009.01.01
  • 발행 : 2010.09.01
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초록

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.

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참고문헌

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피인용 문헌

  1. Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations vol.14, pp.2, 2017, https://doi.org/10.1007/s00009-017-0889-7
  2. Positive solutions to singular system with four-point coupled boundary conditions vol.386, pp.2, 2012, https://doi.org/10.1016/j.jmaa.2011.08.039
  3. On two systems of non-resonant nonlocal boundary value problems vol.21, pp.3, 2013, https://doi.org/10.2478/auom-2013-0057
  4. System of nonlocal resonant boundary value problems involving p-Laplacian vol.68, pp.4, 2018, https://doi.org/10.1515/ms-2017-0149