Existence of nonnegative solutions for discrete Robin boundary value problems with sign-changing weight
نویسندگان
چکیده
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 sign-changing function,~$f:[0,+\infty)\rightarrow[0,+\infty)$~is continuous and nondecreasing function.~$\Delta u(t)=u(t+1)-u(t)$,~$\Delta^{2}u(t)=\Delta(\Delta u(t))$.~By using iterative method Schauder's fixed point theorem,~we will show existence of nonnegative solutions to above problem. Furthermore, we obtain for Robin systems indefinite weights.
منابع مشابه
On the existence of nonnegative solutions for a class of fractional boundary value problems
In this paper, we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation. By applying Kranoselskii`s fixed--point theorem in a cone, first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela--Ascoli theorem is used to take $C^1$ ...
متن کاملExistence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems
متن کامل
Existence of multiple solutions for Sturm-Liouville boundary value problems
In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.
متن کاملExistence of positive solutions for fourth-order boundary value problems with three- point boundary conditions
In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...
متن کاملon the existence of nonnegative solutions for a class of fractional boundary value problems
in this paper, we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation. by applying kranoselskii`s fixed--point theorem in a cone, first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function. then the arzela--ascoli theorem is used to take $c^1$ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Turkish Journal of Mathematics
سال: 2021
ISSN: ['1303-6149', '1300-0098']
DOI: https://doi.org/10.3906/mat-2012-34