DOI QR코드

DOI QR Code

EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SYSTEM OF EVEN ORDER DYNAMIC EQUATION ON TIME SCALES

RAO, SABBAVARAPU NAGESWARA

  • 투고 : 2014.09.23
  • 심사 : 2015.02.23
  • 발행 : 2015.09.30

초록

We determine interval of two eigenvalues for which there existence and nonexistence of positive solution for a system of even-order dynamic equation on time scales subject to Sturm-Liouville boundary conditions.

키워드

System of equations;time scales;eigenvalue intervals;positive solutions;existence;nonexistence;cone

참고문헌

  1. R. Luca and C. Deliu, Nonexistence of positive solutions for a system of higher-order multi-point boundary value problems, ROMAI J. 9 (2013), 69-77.
  2. H.R. Sun, Existence of positive solutions to second-order time scale systems, Comp. Math. Appl. 49 (2005), 131-145. https://doi.org/10.1016/j.camwa.2005.01.011
  3. H. Wang, On the number of positive solutions of nonlinear systems, J. Math. Anal. Appl. 281 (2003), 287-306. https://doi.org/10.1016/S0022-247X(03)00100-8
  4. Y. Zhou and Y. Xu, Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations, J. Math. Anal. Appl. 320 (2006), 578-590. https://doi.org/10.1016/j.jmaa.2005.07.014
  5. J. Henderson, S.K. Ntouyas and I.K. Purnaras, Positive solutions for systems of threepoint nonlinear boundary value problems with deviating arguments, CUBO A Math. J. 11 (2009), 79-100.
  6. L.H. Erbe and A. Peterson, Positive solutions for a nonlinear differential equation on a measure chain, Math. Comp. Modell. 32 (2000), 571-585. https://doi.org/10.1016/S0895-7177(00)00154-0
  7. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.
  8. S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results in Math. 18 (1990), 18-56. https://doi.org/10.1007/BF03323153
  9. J. Henderson and R. Luca, Existence of positive solutions for a system of higher-order multi-point boundary value problems, Appl. Math. Comput. 219 (2012), 3709-3720. https://doi.org/10.1016/j.amc.2012.10.001
  10. J. Henderson and R. Luca, Positive solutions for a system of second order multi-point boundary value problem, Appl. Math. Comput. 218 (2012), 10572-10585. https://doi.org/10.1016/j.amc.2012.04.019
  11. M.A. Krasnosel'skii, Positive solutions of operator equations, P. Noordhoff Ltd, Groningen, The Netherlands, 1964.
  12. A. Kameswararao and S. Nageswararao, Eigenvalue problems for systems of nonlinear boundary value problems on time scales, Int. J. Diff. Equn. 7 (2012), 179-194.
  13. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time scales, Birkhauser, Boston, 2003.
  14. C.J. Chyan and J. Henderson, Eigenvalue problems for nonlinear differential equations on a measure chain, J. Math. Anal. Appl. 245 (2000), 547-559. https://doi.org/10.1006/jmaa.2000.6781
  15. D.R. Anderson, Eigenvalue intervals for a second-order mixed-conditions problem on time scale, Int. J. Nonlinear Diff. Eqns. 7 (2002), 97-104.
  16. D.R. Anderson, Eigenvalue intervals for a two-point boundary value problem on a measure chain, J. Comp. Appl. Math. 141 (2002), 57-64. https://doi.org/10.1016/S0377-0427(01)00435-6
  17. D.R. Anderson, Eigenvalue intervals for even-order Sturm-Liouville Dynamic equations, Comm. Appl. Nonlinear Anal. 12 (2005), 1-13.
  18. M. Bohner and A. Peterson, Dynamic Equations on Time Scales : An Introduction with Applications, Birkhauser, Boston, 2001.