*Mathematical Methods in the Applied Sciences*Global structure and one-sign solutions for second-order Sturm-Liouville
difference equation with sign-changing weight

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 2020

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14 Apr 2021