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In this paper, using the theory of fixed point index on a cone and the Leray-Schauder fixed point theorem, we present the multiplicity of positive solutions for the singular nonlocal boundary-value problems involving nonlinear integral conditions and the existence of at least one positive solution for the singular nonlocal boundary-value problems with sign-changed nonlinearities. [ABSTRACT FROM AUTHOR]

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]

In this paper, Krasnoselskii's theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals. [ABSTRACT FROM AUTHOR]

Using a specially constructed cone and the fixed point index theory, this paper shows the existence of multiple positive solutions for a class of nonresonant singular boundary-value problem of second-order differential equations. The nonexistence of positive solution is also studied. [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]