Proyecciones Journal of Mathematics Vol. 35, N^o 1, pp. 99-117, March 2016. Universidad Católica del Norte Antofagasta - Chile

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

Imran Talib

Naseer Ahmad Asif

University of Management and Tech.

Pakistán

Cemil Tunc

Yuzuncu Yil University

Turkey

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ABSTRACT

The present article investigates the existence of Solutions of the following nonlinear second order coupled system with nonlinear coupled boundary conditions (CBCs)

 

where f₁,f₂    :    [0,1] x R → R,     μ:  R⁶  →  R²    and υ : 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 estab-lishing the arguments. Some examples are taken to ensure the validity of the theoretical results.

Keywords : Lower and upper solutions, Nonlinear coupled system, Coupled nonlinear boundary conditions, Arzela-Ascoli theorem, Schauder’s fixed point theorem.

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Imran Talib

School of Science,

Department of Mathematics,

University of Management and Technology, CII Johar Town, Lahore,

Pakistan

e-mail : imrantaalib@gmail.com

Naseer Ahmad Asif

School of Science,

Department of Mathematics,

University of Management and Technology, CII Johar Town, Lahore,

Pakistan

e-mail : naseerasif@yahoo.com

Cemil Tunc

Department of Mathematics Faculty of Sciences,

Yuzuncu Yil University,

Van,

Turkey

e-mail : cemtunc@yahoo.com

Received : November 2015. Accepted : January 2016