Existence of multiple positive solutions of singular nonlinear boundary value problems

For a given positive integer N, we provide conditions on the nonlinear function f which guarantee that the boundary value problem

     

Existence of positive solutions for singular boundary value problems involving the one-dimensional p-Laplacian

This paper studies the existence of positive solutions for singular Dirichlet boundary value problems. These results are obtained by using the Global continuation theorem, fixed point index theory and approximate method.     

Existence and multiplicity of positive solutions for an elastic beam equation

This paper investigates the boundary value problem for elastic beam equation of the form

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

Positive and dead core solutions of singular BVPs for third-order differential equations

The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u^″))^′=λf(t,u,u^′,u^″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y.     

A necessary and sufficient condition for the existence of positive solutions to a kind of singular three-point boundary value problem

In this paper, we are concerned with the following three point boundary value problem

     

Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nth-order singular nonlocal boundary value problem

     

Existence results of periodic solutions for third‐order nonlinear singular differential equation

Using Green's function for third‐order differential equation and some fixed‐point theorems, i.e., Leray‐Schauder alternative principle and Schauder's fixed point theorem, we establish three new existence results of periodic solutions for nonlinear third‐order singular differential equation, which extend and improve significantly existing results in the literature.     

Existence and multiplicity results for nonlinear nonautonomous second-order systems

In this paper we consider nonlinear periodic systems driven by the ordinary p$p$-Laplacian and having a nonsmooth potential function. Under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (i.e. it is unbounded both above and below).     

An existence theorem of positive solutions for elastic beam equation with both fixed end-points

Abstract. By using the degree theory on cone an existence theorem of positive solution for aclass of fourth-order two-point BVP‘s is obtained. This class of BVP‘s usually describes the de-formation of the elastic beam with both fixed end-points.