Sentence examples similar to discrete third from inspiring English sources

In this paper, we consider the existence of positive solutions for a discrete third-order boundary value problems, which has the sign-changing Green's function.

For the discrete case, there are also several excellent results on the existence of positive solutions of the discrete third-order boundary value problems; see, for instance, [11 16] and the references therein.

Specially, in [12], Agarwal and Henderson considered the following discrete third-order nonlinear eigenvalue problems: left { textstylebegin{array}{l} Delta^{3}u(t)=lambda a(t)f t,u(t)), quad tin[2,T]_{mathbb{Z}}, u(0)=u(1)=u(T+3)=0.

In this paper, we consider the existence of a positive solution for the following discrete third-order BVP: left { begin{array}{l} Delta^{3} u t-1)+a(t)f(t,u t-1=0,quad tin[1,T-1]_{mathbb{Z}}, u(0)=Delta u(T)=Delta^{2}u(eta)=0, end{array} right.

In this paper, by using the Krasnosel'skii fixed point theorem in a cone, we discuss the existence of positive solutions to the discrete third-order three-point boundary value problem left { textstylebegin{array}{l} Delta^{3}u t-1)=lambda a(t)f t,u(t)), quad tin[1,T-2]_{mathbb{Z}}, Delta u(0)=u(T =Delta^{2}u eta)=0, end{array}displaystyle right.

with the discrete second derivative operator.

Consider the following discrete fourth-order Lidstone problem: (4.1).

Hence, we conclude with an equivalent form of discrete second derivative as (16).

These lemmas are based on the linear discrete fourth-order equation.

Consider the following discrete second-order two-point boundary value problem (BVP for short): (1.1).

Clearly, system (5) is also a discrete second order Hamiltonian system.