Uniqueness of positive solutions for Sturm-Liouville boundary value problems

Sufficient conditions for the uniqueness of positive solutions of singular Sturm-Liouville boundary value problems

where and , are established.

     

Uniqueness and parameter dependence of positive solutions to higher order boundary value problems with fractional $q$-derivatives

The authors study a class of nonlinear higher order boundary value problem with fractional $q$-erivativesand dependence on a positive parameter $\lm$.The existence, uniqueness, and dependence of positive solutions on $\lm$ are discussed.Two sequences are constructed so that they converge uniformly to the unique solution of the problems.Two examples are included in the paper. Numerical computations of the examples confirm their theoretical results.     

The existence of positive solutions for some nonlinear boundary value problems with linear mixed boundary conditions

In this paper we study the existence of positive solutions of the equation

(φ(x^′)^)′+a(t)f(x(t))=0,     

Positive solutions of multi-point boundary value problems at resonance

We establish new results on the existence of positive solutions for some multi-point boundary value problems at resonance. Our results are based on a recent Leggett–Williams norm-type theorem due to O’Regan and Zima. We also derive a new result for a three-point problem, previously studied by several authors.     

Multiple positive solutions of boundary value problems for systems of nonlinear second-order differential equations

This paper is concerned with boundary value problems for systems of nonlinear second-order differential equations. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.     

Multiple positive solutions for a functional second-order boundary value problem

By using the Krasnoselskii fixed point theorem on cones in Banach spaces some existence results of positive solutions of a boundary value problem concerning a second-order functional differential equation are given.     

Existence of positive solutions of Lidstone boundary value problems

We show that there exists at least one positive solution for Lidstone boundary value problem

     

Exact number of positive solutions for semipositone problems

This paper is concerned with the exact number of positive solutions for the boundary value problem ^′(|y^′|^p−2y^′)+λf(y)=0 and y(−1)=y(1)=0, where p>1 and λ>0 is a positive parameter. We consider the case in which both f(u) and g(u)=(p−1)f(u)−uf^′(u) change sign exactly once from negative to positive on (0,∞).     

Multiple positive solutions for discrete nonlocal boundary value problems

In this paper, we investigate a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions. The explicit expressions of the associated Green's functions are presented. By using a recently developed fixed point theorem, we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem.     

Symmetric positive solutions of nonlinear boundary value problems

We study the nonlinear boundary value problem

     

Positive solutions of second-order boundary value problems with sign-changing nonlinear terms

In this paper the existence results of positive solutions are obtained for second-order boundary value problem

−u″=f(t,u),t∈(0,1),u(0)=u(1)=0,     

Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation (?p^′(u^′))+q(t)f(t,u,u^′)=0, t∈(0,1), subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems.     

Uniqueness of positive solutions of a class of quasilinear ordinary differential equations

Abstract. Uniqueness results are obtained for positive solutions of a class of quasilinear ordi-nary differential equations. The methods rely on the energy analysis and a scale argument.     

Branches of positive and free boundary solutions for some singular quasilinear elliptic problems

We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms.     

On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations: