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- Title
Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem.
- Authors
Bo Zheng; Huafeng Xiao
- Abstract
This paper studies the existence of multiple solutions of the second-order difference boundary value problem Δ²u(n - 1) + V′(u(n)) = 0, n ε ℤ(1, T), u(0) = 0 = u(T + 1). By applying Morse theory, critical groups, and the mountain pass theorem, we prove that the previous equation has at least three nontrivial solutions when the problem is resonant at the eigenvalue λk (k ≥ 2) of linear difference problem Δ²u(n - 1) + λu(n) = 0, n ε ℤ(1, T), u(0) = 0 = u(T + 1) near infinity and the trivial solution of the first equation is a local minimizer under some assumptions on V .
- Subjects
BOUNDARY value problems; DIFFERENTIAL equations; NUMERICAL analysis; INTEGRAL theorems; EIGENVALUES; HOUGH functions
- Publication
International Journal of Mathematics & Mathematical Sciences, 2010, p1
- ISSN
0161-1712
- Publication type
Article
- DOI
10.1155/2010/907453