East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SOLVABILITY FOR A SYSTEM OF MULTI-POINT BOUNDARY VALUE PROBLEMS ON AN INFINITE INTERVAL

  • Jeong, Jeongmi (Department of mathematics, Pusan National University) ;
  • Lee, Eun Kyoung (Department of Mathematics Education, Pusan National University)
  • Received : 2014.09.04
  • Accepted : 2015.03.17
  • Published : 2015.05.31
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Abstract

The existence of at least one solution to a system of multipoint boundary value problems on an infinite interval is investigated by using the Alternative of Leray-Schauder.

Keywords

References

  1. R. P. Agarwal and D. O'Regan, I nfinite interval problems for differential, difference and integral equations, Kluwer Academic Publishers, Dordrecht, 2001.
  2. F. V. Atkinson and L. A. Peletier, Ground states of ${\Delta}u$ = f(u) and the Emden-Fowler equation, Arch. Rational Mech. Anal. 93 (1986), no. 2, 103-127. https://doi.org/10.1007/BF00279955
  3. A. V. Bicadze and A. A. Samarskii, Some elementary generalizations of linear elliptic boundary value problems, Dokl. Akad. Nauk SSSR 185 (1969), 739-740.
  4. K. Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596. Springer-Verlag, Berlin, 1977.
  5. S. Djebali and K. Mebarki, System of singular second-order differential equations with integral condition on the positive half-line, Electron. J. Qual. Theory Differ. Equ. (2013), no. 50, 1-42.
  6. L. Erbe and K. Schmitt, On radial solutions of some semilinear elliptic equations, Differential Integral Equations 1 (1988), no. 1, 71-78.
  7. A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathematics. Springer-Verlag, New York, 2003.
  8. D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear integral equations in abstract spaces, volume 373 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1996.
  9. C. Gupta, Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl. 168 (1992), no. 2, 540-551. https://doi.org/10.1016/0022-247X(92)90179-H
  10. V. A. Il'in and E. I. Moiseev, A nonlocal boundary value problem of the second kind for the Sturm-Liouville operator, Differental Equations 23 (1987), 979-987.
  11. W. Jiang, Solvability for p-laplacian boundary value problem at resonance on the half-line, Boundary Value Problems (2013), no. 207, 1-10.
  12. C.-G. Kim, Existence and iteration of positive solutions for multi-point boundary value problems on a half-line, Comput. Math. Appl. 61 (2011), no. 7, 1898-1905. https://doi.org/10.1016/j.camwa.2011.02.023
  13. C.-G. Kim, Solvability of multi-point boundary value problems on the half-line, J. Nonlinear Sci. Appl. 5 (2012), no. 1, 27-33.
  14. N. Kosmatov, Multi-point boundary value problems on an unbounded domain at resonance, Nonlinear Anal. 68 (2008), no. 8, 2158-2171. https://doi.org/10.1016/j.na.2007.01.038
  15. N. Kosmatov, Second order boundary value problems on an unbounded domain, Nonlinear Anal. 68 (2008), no. 4, 875-882. https://doi.org/10.1016/j.na.2006.11.043
  16. H. Lian and W. Ge, Solvability for second-order three-point boundary value problems on a half-line, Appl. Math. Lett. 19 (2006), no. 10, 1000-1006. https://doi.org/10.1016/j.aml.2005.10.018
  17. S. Liang and J. Zhang, Positive solutions for singular third-order boundary value problem with dependence on the first order derivative on the half-line, Acta Appl. Math. 111 (2010), no. 1, 27-43. https://doi.org/10.1007/s10440-009-9528-z
  18. J. Mawhin, Topological degree methods in nonlinear boundary value problems, volume 40 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence, R.I., 1979.
  19. S. McArthur and N. Kosmatov, A note on the second order boundary value problem on a half-line, Electron. J. Qual. Theory Differ. Equ. (2009), no. 21, 1-8.
  20. D. O'Regan, B. Yan, and R. P. Agarwal, Solutions in weighted spaces of singular boundary value problems on the half-line, J. Comput. Appl. Math. 205 (2007), no. 2, 751-763. https://doi.org/10.1016/j.cam.2006.02.055
  21. J. Xu and Z. Yang, Positive solutions for singular Sturm-Liouville boundary value problems on the half line, Electron. J. Differential Equations (2010), no. 171, 1-8 pp.
  22. B. Yan, D. O'Regan, and R. P. Agarwal, Positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals, Acta Appl. Math. 103 (2008), no. 1, 19-57. https://doi.org/10.1007/s10440-008-9218-2
  23. A. Yang, C. Miao, and W. Ge, Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line, Electron. J. Qual. Theory Differ. Equ. (2009), no. 19, 1-15.
  24. X. Zhang, Positive solutions of singular multipoint boundary value problems for systems of nonlinear second-order differential equations on infinite intervals in Banach spaces, Bound. Value Probl. (2009), Art. ID 978605, 1-22.