Abstract
The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.
Highlights
The topic of boundary value problems is an important area of investigation in view of its applications in a variety of disciplines such as modern fluid mechanics [1], nano boundary layer fluid flows [2], conservation laws [3], cellular systems and aging models [4], magnetohydrodynamic flow of a second grade nanofluid over a nonlinear stretching sheet [5] and magneto Maxwell nano-material by a surface of variable thickness [6]
In order to cope with this situation, the concept of nonlocal boundary conditions serves as an excellent tool
We have presented the sufficient criteria for the existence and uniqueness of solutions for a coupled system of self-adjoint nonlinear second-order ordinary differential equations supplemented with nonlocal multi-point coupled boundary conditions on an arbitrary domain
Summary
Hari Mohan Srivastava 1,2,3,4, *,† , Sotiris K. Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy.
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