DOI QR코드

DOI QR Code

MULTIPLICITY RESULTS FOR A CLASS OF SECOND ORDER SUPERLINEAR DIFFERENCE SYSTEMS

  • Zhang, Guoqing (COLLEGE OF SCIENCE, UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY) ;
  • Liu, Sanyang (COLLEGE OF SCIENCE, XIDIAN UNIVERSITY)
  • Published : 2006.11.30

Abstract

Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems $$(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0$$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, ${\Delat}x(k)=x(k+1)-x(k)$ is the forward difference operator and ${\Delta}^2x(k)={\Delta}({\Delta}x(k))$.

Keywords

References

  1. R. P. Agarwal, Difference equations and inequalities, in: Monographs and Text-books in Pure and Applied Mathematics, Vol. 228, Marcel Dekker Inc., New York, 2000
  2. R. P. Agarwal, K. Perera, and D. ORegan, Multiple positive solutions of singular and nonsingular discrete problems via variational methods, Nonlinear Anal. 58 (2004), no. 1-2, 69-73 https://doi.org/10.1016/j.na.2003.11.012
  3. K. C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhauser Boston, Inc., Boston, 1993
  4. Z. M. Guo and J. S. Yu, The existence of periodic and subharmonic solutions for a class of second order superlinear, difference equation, Science in China (Series A), 33 (2003), 226-235
  5. P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, Vol. 65, American Mathematical Society, 1986

Cited by

  1. Nontrivial solutions for resonant difference systems via computations of the critical groups vol.385, pp.1, 2012, https://doi.org/10.1016/j.jmaa.2011.06.027
  2. Nontrivial solutions of a second order difference systems with multiple resonance vol.218, pp.18, 2012, https://doi.org/10.1016/j.amc.2012.03.017