Positive solutions for systems of a nonlinear fourth-order singular semipositone Sturm-Liouville boundary value problem

This paper concerns the existence of positive solutions for systems of a fourth-order singular semipositone Sturm-Liouville boundary value problem. By applying the fixed point index theorem, some sufficient conditions for positive solutions are established. An example is given to demonstrate the application of our main results.     

Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems

We consider the existence of positive solutions for the following fourth-order singular Sturm-Liouville eigenvalue problems

     

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.     

Positive solutions of nonlinear singular third-order two-point boundary value problem

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem

     

Positive solutions of a singular nonlinear third order two-point boundary value problem

In this paper some existence results of positive solutions for the following singular nonlinear third order two-point boundary value problem:

     

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.     

Positive solutions of some nonlocal fourth-order boundary value problem

By the use of the Krasnosel’skii’s fixed point theorem, the existence of one or two positive solutions for the nonlocal fourth-order boundary value problem

     

Positive solutions for a singular fractional boundary value problem

We investigate the existence of positive solutions for a system of Riemann-Liouville fractional differential equations, supplemented with uncoupled nonlocal boundary conditions which contain various fractional derivatives and Riemann-Stieltjes integrals, and the nonlinearities of the system are nonnegative functions and they may be singular at the time variable. In the proof of our main theorems, we use the Guo-Krasnosel'skii fixed point theorem.     

Nodal solutions for a nonlinear fourth-order eigenvalue problem

We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa（x）f（y）,0〈x〈1,y（0）=y（1）=y″（0）=y″（1）=0where λ is a positive parameter, a ∈ C（[0, 1], （0, ∞）, f ∈C（R,R） satisfies f（u）u 〉 0 for all u ≠ 0. We give conditions on the ratio f（s）/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.     

Positive solutions for nonlinear singular boundary value problems

Some sufficient conditions for the existence of positive solutions to Dirichlet boundary value problems of a class of nonlinear second order differential equations are given.     

Positive solutions of singular third-order three-point boundary value problem

In this paper we investigate the problem of existence of positive solutions for the nonlinear singular third-order three-point boundary value problem

     

Positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays

The paper is concerned with the delay differential equation u^″+λb(t)f(u(t−τ))=0 satisfying u(t)=0 for −τ?t?0 and , where denotes the Riemann-Stieltjes integral. By applying the fixed point theorem in cones, we show the relationship between the asymptotic behaviors of the quotient (at zero and infinity) and the open intervals (eigenvalue intervals) of the parameter λ such that the problem has zero, one and two positive solution(s). If g(t)=t, by using a property of the Riemann-Stieltjes integral, the above nonlocal boundary value problem educes a three-point boundary value problem with delay, for which some similar results are established.     

Positive solutions and eigenvalue intervals for nonlinear systems

This paper deals with the existence of positive solutions for the nonlinear system