Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 760-766.

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Existence and Multiplicity of Solutions for a 2$n$th-Order Discrete Boundary Value Problems with a Parameter

Zhenguo Wang()   

  1. School of Mathematics and Statistics, Huanghuai University, Henan Zhumadian 463000
  • Received:2021-05-20 Online:2022-06-26 Published:2022-05-09
  • Supported by:
    the NSFC(11971126);the Program for Scientific and Technological Research of Lüliang City(Rc2020213)


In this paper, we consider the existence and multiplicity of solutions for a $2n$th-order discrete boundary value problems depending on a parameter $\lambda$. When $\lambda\in\left(\frac{p(T)}{2B}, \frac{1}{2A}\right)$, we obtain a sufficient condition for the existence of solutions of a discrete boundary value problems by means of critical point theory. Finally, one example is given to illustrate our main result.

Key words: Difference equation, Boundary value problems, Critical point theory, Nontrivial solutions

CLC Number: 

  • O175.8