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On a first-order differential system with initial and nonlocal boundary conditions

Ngoc Le Thi Phuong, Long Nguyen Thanh

Demonstratio Mathematica

2022

Vol. 55, nr 1

277--296

This paper is devoted to the existence of solutions and the multiplicity of positive solutions of an initial-boundary value problem for a nonlinear first-order differential system with nonlocal conditions. The main tool is the fixed-point theorem in which we construct the novel representation of the associated Green’s functions with useful properties and define a cone in the Banach space suitably. Some examples are also given to demonstrate the validity of the main results.

Positive solutions for discrete boundary value problems with p-Laplacian

Ji D., Ge W.

Journal of Applied Analysis

2010

Vol. 16, nr 1

107-119

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following two-point discrete boundary value problem with p-Laplacian: Δ(∅p(Δu(k - 1))) + e(k)f(u(k)) = 0 , k∈ N(1,T) , u(0) - B0 (Δu(0)) = 0 , u(T + 1) + B1 (Δu(T)) = 0. The main tool is the monotone iterative technique.