On the existence and nonexistence of positive solutions for nonlinear Sturm-Liouville boundary value problems

In this paper the existence and nonexistence results of positive solutions are obtained for Sturm-Liouville boundary value problem

     

Positive solutions for singular semi-positone boundary value problems

In this paper, some new results about the existence of positive solutions for singular semi-positone boundary value problems are obtained. The results of this paper partially improve the former corresponding work.     

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 fourth-order boundary value problems with two parameters

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

u(4)+βu″−αu=f(t,u),0<t<1,u(0)=u(1)=u″(0)=u″(1)=0,     

Positive solutions of m-point boundary value problems

The second-order m-point boundary value problem

     

Positive solutions for systems of a nonlinear fourth-order singular semipositone boundary value problems

In this paper, we study the existence of positive solutions of a two-point boundary value problem for a system of fourth-order nonlinear singular semipositone differential equations by the fixed point index theorem. Some new existence results are established, and an example is given to demonstrate the application of our main results.     

Existence of positive solutions for second-order boundary value problem with one parameter

In the case of not requiring f(t,u) to be nonnegative, by transforming the boundary value problem into the integral equation system, and applying the fixed point index theory, the author studies the following second-order boundary value problem with one parameter

     

On existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system

By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system. Some well-known results in the literature are generalized and improved. An example is presented to illustrate the application of our main result.     

Positive solutions for nonlinear three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T. Consider the following three-point boundary value problem on time scales:

     

A note on singular nonlinear boundary value problems

In this paper we study the existence and multiplicity of solutions of the following operator equation in Banach space E:

u=λAu,0<λ<+∞,u∈P?{θ},     

Existence of positive solutions for Sturm-Liouville boundary value problems on the half-line

In this paper, we establish sufficient conditions to guarantee the existence of at least one positive solution, a unique positive solution, and multiple positive solutions for the Sturm-Liouville boundary value problem on the half-line. By using an effective operator, the fixed point theorems in cone, especially Krasnoselskii fixed point theorem, can be applied to such systems and then existence criteria are established. The interesting point of the results is that the nonlinear term f can be sign-changing.     

Necessary and sufficient conditions for the existence of symmetric positive solutions of singular boundary value problems

Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem

     

Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T, β,γ?0 and 0<η<ρ(T). We consider the following p-Laplacian three-point boundary problem on time scales

     

Positive solutions for fourth-order singular p -Laplacian boundary value problems

This article investigates fourth-order singular p-Laplacian boundary value problems (BVPs), and obtains the necessary and sufficient conditions for existence of positive solutions for fourth-order singular p-Laplacian BVPs on closed interval.     

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.     

Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces

The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray-Schauder type and on a fixed point theorem in cones.     

Positive solutions of nonlinear three-point boundary-value problems

Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ₁(t) be the unique solution of the linear boundary value problem

u″(t)+a(t)u′(t)+b(t)u(t)=0,t∈(0,1),u(0)=0,u(1)=1.     

Existence of multiple symmetric positive solutions of higher order Lidstone problems

This paper gives the sufficient conditions of the existence of at least three symmetric positive solutions for one type of higher order autonomous Lidstone problem by applying the five functionals fixed point theorem. The analogous result for higher order nonautonomous singular Lidstone problem is also proved here.     

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,