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Global structure and one-sign solutions for second-order Sturm-Liouville difference equation with sign-changing weight
  • fumei ye
fumei ye
Northwest Normal University

Corresponding Author:[email protected]

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Abstract

This paper is devoted to study the discrete Sturm-Liouville problem $$ \left\{\begin{array}{ll} -\Delta(p(k)\Delta u(k-1))+q(k)u(k)=\lambda m(k)u(k)+f_1(k,u(k),\lambda)+f_2(k,u(k),\lambda),\ \ k\in[1,T]_Z,\\[2ex] a_0u(0)+b_0\Delta u(0)=0,\ a_1u(T)+b_1\Delta u(T)=0, \end{array}\right. $$ where $\lambda\in\mathbb{R}$ is a parameter, $f_1, f_2\in C([1,T]_Z\times\mathbb{R}^2, \mathbb{R})$, $f_1$ is not differentiable at the origin and infinity. Under some suitable assumptions on nonlinear terms, we prove the existence of unbounded continua of positive and negative solutions of this problem which bifurcate from intervals of the line of trivial solutions or from infinity, respectively.
08 Dec 2020Submitted to Mathematical Methods in the Applied Sciences
09 Dec 2020Submission Checks Completed
09 Dec 2020Assigned to Editor
21 Dec 2020Reviewer(s) Assigned
14 Apr 2021Review(s) Completed, Editorial Evaluation Pending
15 Aug 2021Editorial Decision: Revise Minor
16 Aug 20211st Revision Received
16 Aug 2021Submission Checks Completed
16 Aug 2021Assigned to Editor
18 Aug 2021Reviewer(s) Assigned
23 Aug 2021Review(s) Completed, Editorial Evaluation Pending
31 Aug 2021Editorial Decision: Accept
Feb 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 3 on pages 1176-1188. 10.1002/mma.7844