East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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POSITIVE SOLUTIONS FOR THE SECOND ORDER DIFFERENTIAL SYSTEM WITH STRONGLY COUPLED INTEGRAL BOUNDARY CONDITION

  • You-Young Cho (Department of Mathematics, Pusan National University) ;
  • Jinhee Jin (Department of Mathematics, Pusan National University) ;
  • Eun Kyoung Lee (Department of Mathematics Education, Pusan National University)
  • Received : 2023.11.21
  • Accepted : 2023.12.13
  • Published : 2024.01.31
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Abstract

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

Keywords

Acknowledgement

This work was supported by a 2-Year Research Grant of Pusan National University.

References

  1. J.R. Cannon, The solution of the heat equation subject to the specification of energy, Quart. Appl. Math. 21 (1963), no. 2, 155-160. https://doi.org/10.1090/qam/160437
  2. R. Yu. Chegis, Numerical solution of a heat conduction problem with an integral boundary condition, Litovsk. Mat. Sb. 24 (1984), 209-215.
  3. X. Cheng and C. Zhong, Existence of positive solutions for a second-order ordinary differential system, J. Math. Anal. Appl. 312 (2005), no. 1, 14-23. https://doi.org/10.1016/j.jmaa.2005.03.016
  4. 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.
  5. Y. Cui, W. Ma, X. Wang and X. Su, Uniqueness theorem of differential system with coupled integral boundary conditions, Electron. J. Qual. Theory Differ. Equ. (2018), no. 9, 1-10.
  6. 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
  7. 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.
  8. 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.
  9. G. Infante and P. Pietramala, Eigenvalues and nonnegative solutions of a system with nonlocal BCs, Nonlinear Stud. 16 (2009), no.2, 187-196.
  10. N.I. Ionkin, Solution of a boundary value problem in heat conduction theory with nonlocal boundary conditions, Diff. Equ. 13 (1977), 294-304.
  11. M. A. Krasnosel'skii, Positive solutions of operator equations, P. Noordhoff, Groningen, The Netherlands, 1964.
  12. 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.
  13. Z.L. Yang, Positive solutions to a system of second-order nonlocal boundary value problems, Nonlinear Anal. 62 (2005), no. 7, 1251-1265. https://doi.org/10.1016/j.na.2005.04.030
  14. E. Zeidler, Nonlinear Functional Analysis and its Applications I, Springer-Verlag, New York, 1985.