East Asian mathematical journal

  • 제34권5호
  • /
  • Pages.651-660
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  • 2018
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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EXISTENCE OF POSITIVE SOLUTIONS FOR THE SECOND ORDER DIFFERENTIAL SYSTEMS WITH STRONGLY COUPLED INTEGRAL BOUNDARY CONDITIONS

  • Lee, Eun Kyoung (Department of Mathematics Education, Pusan National University)
  • 투고 : 2018.07.30
  • 심사 : 2018.09.10
  • 발행 : 2018.09.30
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초록

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

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참고문헌

  1. M. Feng, D. Ji and W. Ge, Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces, J. Comput. Appl. Math. 222 (2008), no. 2, 351-363. https://doi.org/10.1016/j.cam.2007.11.003
  2. J.M. Gallardo, Second-order differential operators with integral boundary conditions and generation of analytic semigroups, Rocky Mountain J. Math. 30 (2000) no. 4, 1265-1291. https://doi.org/10.1216/rmjm/1021477351
  3. J.R. Cannon, The solution of the heat equation subject to the specification of energy, Quat. Appl. Math. 21 (1963), no. 2, 155-160. https://doi.org/10.1090/qam/160437
  4. R. Yu. Chegis, Numerical solution of a heat conduction problem with an integral boundary condition, Litovsk. Mat. Sb. 24 (1984), 209-215.
  5. N.I. Ionkin, Solution of a boundary value problem in heat conduction theory with nonlocal boundary conditions, Differential Equations 13 (1977), 294-304.
  6. X. Cheng and C. Zhong, Existence of positive solutions for a second-order ordinary differential system, J. Math. Anal. Appl. 312 (2005), 14-23. https://doi.org/10.1016/j.jmaa.2005.03.016
  7. G. Infante and P. Pietramala, Eigenvalues and nonnegative solutions of a system with nonlocal BCs, Nonlinear Stud. 16 (2009), no.2, 187-196.
  8. W.J. Song and W.j. Gao, Positive solutions for a second-order system with integral boundary conditions, Electron. J. Differential Equations, 2011 (2011), no.13, 1-9.
  9. Z.L. Yang, Positive solutions to a system of second-order nonlocal boundary value problems, Nonlinear Anal. 62 (2005), 1251-1265. https://doi.org/10.1016/j.na.2005.04.030
  10. J. Henderson and R. Luca, Positive solutions for systems of second-order integral boundary value problems, Electron. J. Qual. Theory Differ. Equ. (2013), No. 70, 1-21.
  11. Y. Cui and J. Sun, On existence of positive solutions of coupled integral boundary vlaue problems for a nonlinear singular superlinear differential system, Electron. J. Qual. Theory Differ. Equ. (2012), No. 41, 1-13.
  12. D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones, 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press Inc., Boston, MA, 1988.