Existence of solutions to second order nonlinear coupled system with nonlinear coupled boundary conditions
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Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Journal of Differential Equations
Abstract
In this article, study the existence of solutions for the second-order
nonlinear coupled system of ordinary differential equations
u
00(t) = f(t, v(t)), t ∈ [0, 1],
v
00(t) = g(t, u(t)), t ∈ [0, 1],
with nonlinear coupled boundary conditions
φ(u(0), v(0), u(1), v(1), u0
(0), v0
(0)) = (0, 0),
ψ(u(0), v(0), u(1), v(1), u0
(1), v0
(1)) = (0, 0),
where f, g : [0, 1] × R → R and φ, ψ : R6 → R2 are continuous functions. Our
main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and
Schauder’s fixed point theorem. The results presented in this article extend
those in [1, 3, 15].
Description
Keywords
Mathematics
Citation
Asif, N. A., Talib, I., & Tunc, C. (2015). Existence of Solutions to Second Order Nonlinear Coupled System with Nonlinear Coupled Boundary Conditions. Electronic Journal of Differential Equations, 2015(13), 1-11. (Naseer Ahmad Asif and Imran Talib) (IF 0.64 JCR Listed)