Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A NOTE ON THE EXISTENCE OF SOLUTIONS OF HIGHER-ORDER DISCRETE NONLINEAR STURM-LIOUVILLE TYPE BOUNDARY VALUE PROBLEMS

  • Liu, Yuji (Department of Mathematics, Guangdong University of Business Studies)
  • 발행 : 2009.01.31
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초록

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

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참고문헌

  1. R.P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations,Kluwer, Dordrecht, 1998.
  2. R.P. Agarwal, D.O'Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.
  3. L. Kong, Q. Kong and B. Zhang, Positive solutions of boundary value problems for third order functional difference equations, Comput. Math. Appl. 44 (2002), 481-489. https://doi.org/10.1016/S0898-1221(02)00170-0
  4. R.P. Agarwal and J. Henderson, Positive solutions and nonlinear eigenvalue problems for third order difference equations, Comput. Math. Appl. 36 (1998), 347-355. https://doi.org/10.1016/S0898-1221(98)80035-7
  5. J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations, in: P. M. Fitzpertrick, M. Martelli, J. Mawhin, R. Nussbanm(Eds.), Topological Methods for Ordinary Differential Equations, Lecture Notes in Math. 1537, Springer-Verlag, New York/Berlin, 1991.
  6. R. Agarwal and F. Wong, Upper and lower solutions methods for higher order discrete boundary value problems, Math. Inequalities Appl. 4 (1998), 551-557.
  7. S. Qi, Multiple positive solutions to boundary value problems for higher-order nonlinear differential equations in Banach spaces, Acta Math. Appl. Sinica 17 (2001), 271-278. https://doi.org/10.1007/BF02669581
  8. R. Ma, Nonlinear discrete Sturm-Liouville problems at resonance, Nonl. Anal. 67 (2007), 3050-3057. https://doi.org/10.1016/j.na.2006.09.058
  9. Y. Liu, On Sturm-Liouville boundary value problems for second-order nonlinear functional finite difference equations, J. Comput. Appl. Math. doi:10.1016/j.cam.2007.06.003.
  10. J. Rodriguez, Nonlinear discrete Sturm-Liouville problems, J. Math. Anal. Appl. 308 (2005), 380-391. https://doi.org/10.1016/j.jmaa.2005.01.032
  11. Y. Li, On the existence and nonexistence of positive solutions for nonlinear Sturm-Liouville boundary value problems, J. Math. Anal. Appl. 304 (2005), 74-86. https://doi.org/10.1016/j.jmaa.2004.09.007
  12. P. Wong, Multiple fixed sign solutions for a system of difference equations with Sturm-Liouville conditions, J. Comput. Appl. Math. 183 (2005), 108-123. https://doi.org/10.1016/j.cam.2005.01.007