Coupled lower and upper solution approach for the existence of solutions of nonlinear coupled system with nonlinear coupled boundary conditions.
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Date
2016
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Publisher
Proyecciones Journal of Mathematics,
Abstract
The present article investigates the existence of solutions of the following nonlinear second order coupled system with nonlinear coupled boundary conditions (CBCs) ⎧ ⎪⎪⎨ ⎪⎪⎩ −u 00 (t) = f1(t, v(t)), t ∈ [0, 1], −v 00 (t) = f2(t, u(t)), t ∈ [0, 1], µ(u(0), v(0), u0 (0), v0 (0), u0 (1), v0 (1)) = (0, 0), ν(u(0), v(0)) + (u(1), v(1)) = (0, 0), where f1, f2 : [0, 1] × R → R, µ : R6 → R2 and ν : R2 → R2 are continuous functions. 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. Some examples are taken to ensure the validity of the theoretical results.
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Keywords
Mathematics, Lower and upper solutions, Nonlinear coupled system, Coupled nonlinear boundary conditions, Arzela-Ascoli theorem, Schauder’s fixed point theorem.
Citation
Talib, I., Asif, N. A., & Tunc, C. (2016). Coupled lower and upper solution approach for the existence of solutions of nonlinear coupled system with nonlinear coupled boundary conditions. Proyecciones Journal of Mathematics, 35(1), 99-117. (Imran Talib (Mathematics /SSC), Naseer Ahmad Asif, JCR LISTED)