Browsing by Author "Naseer Ahmad Asif"

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    Coupled lower and upper solution approach for the existence of solutions of nonlinear coupled system with nonlinear coupled boundary conditions.
    (Proyecciones Journal of Mathematics,, 2016) Imran Talib; Naseer Ahmad Asif
    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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    Existence of solution for first-order coupled system with nonlinear coupled boundary conditions
    (Boundary Value Problems, 2015) Naseer Ahmad Asif; Imran Talib
    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.
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    Existence of solutions to a second order coupled system with nonlinear coupled boundary conditions
    (American Journal of Applied Mathematics, 2015) Naseer Ahmad Asif; Imran Talib
    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].
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    Existence of solutions to second order nonlinear coupled system with nonlinear coupled boundary conditions
    (Electronic Journal of Differential Equations, 2015) Naseer Ahmad Asif; Imran Talib
    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].