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Turkish Journal of Mathematics
Existence of nonnegative solutions for discrete Robin boundary value problems with sign-changing weight
YAN ZHU
10.3906/mat-2012-34
In this paper,~we are concerned with the following discrete problem first $$\left\{ \begin{array}{ll} -\Delta^{2}u(t-1)=\lambda p(t)f(u(t)), &t\in[1,N-1]_{\mathbb{Z}},\\ \Delta u(0)=u(N)=0,\\ \end{array} \right. $$ where $N>2$~is an integer,~$\lambda>0$~is a parameter,~$p:[1,N-1]_{\mathbb{Z}}\rightarrow\mathbb{R}$~is a sign-changing function,~$f:[0,+\infty)\rightarrow[0,+\infty)$~is a continuous and nondecreasing function.~$\Delta u(t)=u(t+1)-u(t)$,~$\Delta^{2}u(t)=\Delta(\Delta u(t))$.~By using the iterative method and Schauder's fixed point theorem,~we will show the existence of nonnegative solutions to the above problem. Furthermore, we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights.
Robin boundary value problems, Green's function, iterative method, nonnegative solutions, system
ZHU, YAN (2021) "Existence of nonnegative solutions for discrete Robin boundary value problems with sign-changing weight," Turkish Journal of Mathematics: Vol. 45: No. 2, Article 15. https://doi.org/10.3906/mat-2012-34
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/15
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