Existence of solution for first-order coupled system with nonlinear coupled boundary conditions

Abstract

In this article, the existence of solution for the first-order nonlinear coupled system of ordinary differential equations with nonlinear coupled boundary condition (CBC for short) is studied using a coupled lower and upper solution approach. Our method for a nonlinear coupled system with nonlinear CBC is new and it unifies the treatment of many different first-order problems. Examples are included to ensure the validity of the results.

Existence of solutions for a coupled system with ∅-Laplacian operators and nonlinear coupled boundary conditions

“…Therefore, using Lemmas 3 and 4, (U 1 , U 2 ) is also a solution of problem (1)- (2). By Theorem 1, we deduce existence of at least one solution of the system (12).…”

“…In 2015, Naseer Ahmad Asif and Imran Talib studied in [1], problem (1)-(2), for f i , i ∈ {1, 2} continuous and φ 1 (x) = φ 2 (x) = x, ∀x ∈ R. They proved under some monotony conditions upon g and h, an existence result using a new concept of coupled lower and upper solutions.…”

“…The concept of coupled lower and upper solutions was used by several authors (see [2], [6], [7], [8]). …”

Coupled lower and upper solution approach for the existence of Solutions of nonlinear coupled system with nonlinear coupled boundary conditions

“…The results presented in [7,11] are extended in our article. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder's fixed point theorem play an important role in establishing the arguments.…”

“…The study of ordinary differential systems (ODSs) with coupled and non-coupled boundary conditions has also attracted many authors. The reader can study [4,5,6,7,24,25] and references therein. A second order ordinary differential system (ODS) firstly appeared from the study of chemical reactors [8].…”