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This article considers elliptic problems of Kirchhoff-type. We give some new definitions of lower and upper solutions for the problem and establish the method of lower and upper solutions when the upper and lower solutions are well ordered, i.e., the lower solution is less than the upper one, and we also consider the case when the upper and lower solutions have opposite ordering. In addition we use the relation between the topological degree and strict upper and lower solutions in both cases and using this we obtain multiplicity results for nonlinear Kirchhoff-type elliptic problems. [ABSTRACT FROM AUTHOR]

In this paper we discuss the existence of a solution between well-ordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1. [ABSTRACT FROM AUTHOR]

In this article, using the sub-supersolution method and Rabinowitz- type global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems. [ABSTRACT FROM AUTHOR]

In this article, we study the structure of global solutions to the boundary-value problem ... are continuous. By a comparison principle and spectral properties of the corresponding linear equations, we prove the existence of solutions by using Rabinowitz-type global bifurcation theorems, and obtain results on the behavior of positive solutions for large λ when f(x) = xp+1. [ABSTRACT FROM AUTHOR]

In this article, we consider the singular elliptic boundary-value problem...Using the upper-lower solution method, we show the existence and uniqueness of the solution. Also we study the boundary behavior and asymptotic behavior of the positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign. [ABSTRACT FROM AUTHOR]

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]

This paper considers the existence of positive solutions of the boundary value problems Vn +λ(V +Vp -Vq) = 0 and V(-1) = V(1) = 0, where p > r > q > -1 and λ is a positive parameter. Using a time-map approach, we obtain the exact number of positive solutions in different cases. [ABSTRACT FROM AUTHOR]

This article presents global properties and existence of multiple solutions for a class of boundary value problems of impulsive differential equations. We first show that the spectral properties of the linearization of these problems are similar to the well-know properties of the standard Sturm-Liouville problems. These spectral properties are then used to prove two Rabinowitz-type global bifurcation theorems. Finally, we use the global bifurcation theorems to obtain multiple solutions for the above problems having specified nodal properties. [ABSTRACT FROM AUTHOR]

In this article, we study the existence and uniqueness of the positive solution for a second-order singular three-point boundary-value problem with sign-changing nonlinearities. Our main tool is a fixed-point theorem. [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]

Abstract  The existence of at least one positive solution and the existence of multiple positive solutions are established for the singular second-order boundary value problem $$\left\{\begin{array}{l}{\frac{1}{p(t)}(p(t)x'(t))'}+\Phi(t)f(t,x,px')=0,\quad 0 using the fixed point index, where f may be singular at x=0 and px′=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]

Positive solutions to the singular initial-boundary value problems x″ = - f(t, xt), 0 < t < 1, x0 = 0, x(1) = 0, are obtained by applying the Schauder fixed-point theorem, where xt(u) = x(t+u) (0 ≤ t ≤ 1) on [-r, 0] and f(.,.) : (0, 1) × (C+\{0})→R+(C+ = {x ϵ C([-r, 0], R), x(t) ≥ 0, ∀t ϵ [-r, 0]}) may be singular at φ(u) = 0 (-r ≤ u ≤ 0) and t = 0. As an application, an example is given to demonstrate our result. [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]

Abstract  The existence of multiple positive solutions for the singular Dirichlet boundary-value problem $$\begin{array}{*{20}c} {{x^{{\prime \prime }} + \Phi {\left( t \right)}f{\left( {t,x{\left( t \right)},x^{\prime } {\left( t \right)}} \right)} = 0,\,\,\,\,0 is presented by using the fixed point index; here f may be singular at 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]