On the existence of fixed points of a nonlinear operators for a system of boundary value problems

Document Type : Original Article

Authors
Behnaz Farnam 1
Robabeh Sahandi Torogh 2
Sakineh Sahandi Torogh 3
1 Department of Mathematics,Qom University of Technology, Qom, Iran
2 Departmen of Maths, Varamin-Pishva branch, Islamic Azad University, Tehran, Iran
3 Department of University, Varamin-Pishva branch, Islamic Azad University,Tehran
10.22034/maco.5.1.12
Abstract
Recently, a lot of attention has been given to the study of multi points boundary value problems. This paper is mainly concerned with the existence of positive solutions for a class of nonlinear boundary value problems. We obtain at least one positive solution to this problem. We introduce a completely continuous operator such that, the fixed points of this operator are positive soultions of the problem. We establish some theorems to prove the existence of solutions for this system. A completely continuous operator is defined and by using the fixed point theorem in cones, the existence of solutions is proved.

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