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Zbl 1112.39008
Liang, Haihua; Weng, Peixuan
Existence and multiple solutions for a second-order difference boundary value problem via critical point theory.
(English)
[J] J. Math. Anal. Appl. 326, No. 1, 511-520 (2007). ISSN 0022-247X

This paper deals with the existence and multiplicity of solutions to a second-order difference boundary value problem $$\Delta (p_{k-1}\Delta x_{k-1})+q_kx_k+f(k, x_k)=0, \quad k\in [1, N],$$ $$x_0=x_N, \quad p_0\Delta x_0=p_N\Delta x_N.$$ Under some appropriate assumptions, the authors give some sufficient conditions on the existence and multiplicity of solutions for the above mentioned difference boundary value problem. The main tools used here are the classical variational methods and a variant version of a theorem due to {\it D. C. Clark} [Math. J., Indiana Univ. 22, 65--74 (1972; Zbl 0228.58006)].
[Zhiming Guo (Guangzhou)]
MSC 2000:
*39A12 Discrete version of topics in analysis
39A10 Difference equations

Keywords: difference equation; second-order difference boundary value problem; multiple solution; critical point; variational methods

Citations: Zbl 0228.58006

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