Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system

[摘要] In this paper, we study the existence and multiplicity of positive solutions for the differential equations system x + lambda a(1)(t)f(1)(x(t),y(t)) = 0, 0 < t < 1, y + mu a(2)(t) f(2)(x(t),y(t)) = 0, 0 < t < 1, x(0) = 0 = x(1) - alpha(1)x(eta(1)), y(0) = 0 = y(1) - alpha(2)y(eta(2)), where lambda, mu > 0 are parameters, 0 < eta(2) < eta(1) < 1, alpha(1), alpha(2) is an element of (0, 1), a(1) is an element of C([0, 1], [0,infinity )) and f(2) is an element of C([0, infinity) x [0, infinity), [0, infinity)). The system is a semi-positone problem since the nonlinear term f(1) is allowed to take negative values and a2 (t) may change sign on [0, 1]. The results are established via fixed point index theory. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] semi-positone problems;three-point boundary value problems systems;fixed point index