Abstract
Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type , , , , , , , is established. The nonlinearities , are continuous and may be singular at , and/or , while the parameters , satisfy . An example is also included to show the applicability of our result.
Highlights
Multipoint boundary value problems BVPs arise in different areas of applied mathematics and physics
The vibration of a guy wire composed of N parts with a uniform cross-section and different densities in different parts can be modeled as a Multipoint boundary value problem 1
Many problems in the theory of elastic stability can be modeled as Multipoint boundary value problem 2
Summary
Multipoint boundary value problems BVPs arise in different areas of applied mathematics and physics. Existence theory for nonlinear three-point boundary value problems was initiated by Gupta 7. Since the study of nonlinear three-point BVPs has attracted much attention of many researchers, see 8–11 and references therein for boundary value problems with ordinary differential equations and 12 for boundary value problems on time scales. By using fixed point theorem in cone, Yuan et al 26 studied the following coupled system of nonlinear singular boundary value problem:. We generalize the results studied in 25, 26 to the following more general singular system for three-point nonlocal BVPs:. We study the sufficient conditions for existence of positive solution for the singular system 1.3 under weaker hypothesis on f and g as compared to the previously studied results. To the best of our knowledge, existence of positive solutions for a system 1.3 with singularity with respect to dependent variable s has not been studied previously. The system 1.3 has at least one positive solution
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