EXISTENCE AND STRUCTURE OF SOLUTION SETS FOR NONLINEAR DISCRETE BOUNDARY VALUE PROBLEMS WITH SPECTRAL PARAMETERS IN BOUNDARY CONDITIONS

Dandan Chen; Yanqiong Lu; Chengze Wu

doi:10.11948/20260085

2027 Volume 17 Issue 2

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Dandan Chen, Yanqiong Lu, Chengze Wu. EXISTENCE AND STRUCTURE OF SOLUTION SETS FOR NONLINEAR DISCRETE BOUNDARY VALUE PROBLEMS WITH SPECTRAL PARAMETERS IN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 884-907. doi: 10.11948/20260085

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Dandan Chen, Yanqiong Lu, Chengze Wu. EXISTENCE AND STRUCTURE OF SOLUTION SETS FOR NONLINEAR DISCRETE BOUNDARY VALUE PROBLEMS WITH SPECTRAL PARAMETERS IN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 884-907. doi: 10.11948/20260085

EXISTENCE AND STRUCTURE OF SOLUTION SETS FOR NONLINEAR DISCRETE BOUNDARY VALUE PROBLEMS WITH SPECTRAL PARAMETERS IN BOUNDARY CONDITIONS

1.
Northwest Normal University, Lanzhou 730070, China

Author Bio: Email: Chendd3170@126.com(D. Chen); Email: wchengze@126.com(C. Wu)
Corresponding author: Email: luyq8610@126.com(Y. Lu)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12361040, 12461035)

Abstract

Abstract

By using topological degree methods and bifurcation theory, we prove the existence of the solution and the bifurcation structure at infinity of the second-order difference boundary value problems
$ \left\{ \begin{array}{ll} -\Delta^{2}u(k-1)+c(k)u(k)=0,\quad k\in[1,N ]_{\mathbb{Z}}, \\-\Delta u(0)=(\mu_1+\lambda)\sigma(1)u(1)+f(1,u(1))+h(1),\\ \Delta u(N)=(\mu_1+\lambda)\sigma(N+1)u(N+1)+f(N+1,u(N+1))+h(N+1), \end{array} \right. $
where $ \lambda\in\mathbb{R} $ is a constant, $ \mu_1 $ is a spectral parameter, $ \Delta u(k):=u(k+1)-u(k) $ and $ \Delta^{2}u(k-1):=\Delta(\Delta u(k-1)) $ as the forward difference operator and the second difference operator, respectively.
- Existence /
- steklov problem /
- a priori estimate /
- topological degree methods /
- bifurcation at infinity
MSC: 39A27

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References

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