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In this paper, using fixed-point index theory and approximation techniques, we consider the existence and multiplicity of fixed points of some nonlinear operators with singular perturbation. As an application we consider the existence and multiplicity of positive solutions of singular systems of multi-point boundary value problems, which improve the results in the literature. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular m-point boundary value problem {x"(t) + a(t)f(t,x(t), x'(t)) = 0, 0 < t < 1, x'(0) = 0, x(1) = ∑i=1m-2 αix(xi;i), where 0 < ξ1 < ξ2 < ... < ξm-2 < 1, αi ∈ [0, 1), i = 2, ..., m - 2, with 0 < ∑i=1m-2 αi < 1 and f may change sign and may be singular at x = 0 and x' = 0. [ABSTRACT FROM AUTHOR]

nUsing the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular m-point boundary-value problem x"(t)+a(t)f(t,x(t), x' (t)) = 0, 0 ∑i=1m-2ai < 1 and f maybe singular at x = 0 and x' = 0. [ABSTRACT FROM AUTHOR]

Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem x″(t) + a(t)f(t, x(t), x′(t)) = 0, 0 < t < 1, x′(0) = 0, x(1) = αx(η), where 0 < &alpah; < 1, 0 < η < 1, and f may change sign and may be singular at x = 0 and x′ = 0. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: y"(t) + a(t)f(t, y(t), y'(t)) = 0, 0 < t < 1, y'(0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, and f may be singular at y = 0 and y' = 0. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point index, this article discusses the existence of positive solutions for singular second-order boundary value problems, where f may be singular at x = 0 and x'=0, and f may change sign. [ABSTRACT FROM AUTHOR]