Existence of positive solutions for a second-order ordinary differential system☆

By Xiyou Cheng, Chengkui Zhong. 2005

88 citations recorded by the source corpus.

Abstract In this paper we consider the existence of positive solutions for a second-order ordinary differential system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing a cone K 1 × K 2 which is the Cartesian product of two cones in space C [ 0 , 1 ] and computing the fixed point index in K 1 × K 2 , we establish the existence of positive solutions for the system. We remark that, differently from the literature, we deal with our problem on the Cartesian product of two cones, in which the feature of two equations can be exploited better.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a0030329a1c4dc76396be4ac063cbde100299de3

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In Numerical Analysis

1. Fazhan Geng
2. M. Cui
3. Omar Abu Arqub

Citations in the corpus

• Solving a nonlinear system of second order boundary value problems (2007, background): “In [1–5] the authors discussed the existence of solutions to second order systems, including the approximation of solutions via finite difference equations.”