Open Access

Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Advances in Difference Equations20072007:096415

DOI: 10.1155/2007/96415

Received: 19 March 2007

Accepted: 30 May 2007

Published: 31 July 2007


We study the existence of solutions of nonlinear discrete boundary value problems , , , where is the first eigenvalue of the linear problem , , , satisfies some “asymptotic nonuniform” resonance conditions, and for .


Authors’ Affiliations

Department of Mathematics, Northwest Normal University


  1. Kelley WG, Peterson AC: Difference Equations: An Introduction with Applications. Academic Press, Boston, Mass, USA; 1991:xii+455.MATHGoogle Scholar
  2. Iannacci R, Nkashama MN: Nonlinear two-point boundary value problems at resonance without Landesman-Lazer condition. Proceedings of the American Mathematical Society 1989,106(4):943–952.MATHMathSciNetGoogle Scholar
  3. Lloyd NG: Degree Theory, Cambridge Tracts in Mathematics, no. 73. Cambridge University Press, Cambridge, UK; 1978:vi+172.Google Scholar
  4. Rodriguez J: Nonlinear discrete Sturm-Liouville problems. Journal of Mathematical Analysis and Applications 2005,308(1):380–391. 10.1016/j.jmaa.2005.01.032MATHMathSciNetView ArticleGoogle Scholar
  5. Agarwal RP, O'Regan D: Boundary value problems for discrete equations. Applied Mathematics Letters 1997,10(4):83–89. 10.1016/S0893-9659(97)00064-5MATHMathSciNetView ArticleGoogle Scholar
  6. Agarwal RP, O'Regan D: Nonpositone discrete boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 2000,39(2):207–215. 10.1016/S0362-546X(98)00183-7MATHMathSciNetView ArticleGoogle Scholar
  7. Bai D, Xu Y: Nontrivial solutions of boundary value problems of second-order difference equations. Journal of Mathematical Analysis and Applications 2007,326(1):297–302. 10.1016/j.jmaa.2006.02.091MATHMathSciNetView ArticleGoogle Scholar
  8. Rachunkova I, Tisdell CC: Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions. Nonlinear Analysis: Theory, Methods & Applications 2007,67(4):1236–1245. 10.1016/ ArticleGoogle Scholar


© Ruyun Ma. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.