Baoqiang Yan

Positive solutions for singular boundary value problems with sign changing nonlinearities depending on x′ via index theory

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.

Positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence

Abstract In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR POSITONE DIRICHLET PROBLEMS WITH DERIVATIVE DEPENDENCE

The existence of multiple positive solutions is presented for the singular Dirichlet boundary value problems � x �� + � (t) f (t, x(t), |x � (t)|) = 0,

The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

Abstract In this paper we discuss the existence of a solution between wellordered 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.

Fixed-point theorems for nonlinear operators with singular perturbations and applications

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.

Positive solutions for singular nonlocal boundary value problems

In this paper we present some existence results for singular nonlocal boundary value problems. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign.

Positive solutions for singular nonlocal boundary value problems involving nonlinear integral conditions

In this paper, using the fixed point theory on a cone and Leray-Schauder fixed point theorem, we present some existence results for 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.

Positive solutions for the singular nonlocal boundary value problems involving nonlinear integral conditions

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.MSC:34B10, 34B15, 34B18.