Multiple positive solutions of boundary value problems for second-order discrete equations on the half-line

In this paper, we study the existence of multiple positive solutions of boundary value problems for second-order discrete equations Δ² x(n ? 1) ? pΔx(n ? 1) ? qx(n ? 1)+f(n, x(n)) = 0, n ∈ {1,2,…}, αx(0) ? βΔx(0) = 0, x(∞) = 0. The proofs are based on the fixed point theorem in Fréchet space (see Agarwal and O'Regan, 2001, Cone compression and expansion and fixed point theorems in Fréchet spaces with application, Journal of Differential Equations, 171, 412–42).     

Multiple positive solutions for a fourth-order p-Laplacian Sturm-Liouville boundary value problems on time scales

In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scales ﹛[φp(u△△(t))u △△= f(t, u(σ(t))), t ∈ [a, b],α0 u(a)- β0u△(a) = 0, γ0 u(σ(b)) + δ0 u△(σ(b)) = 0,α0(φp(u△△))(a)- β0(φp(u△△))△(a) = 0,γ0(φp(u△△))(σ(b)) + δ0(φp(u△△))△(σ(b)) = 0,where φp(s) is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.     

Positive solutions for multi-point boundary value problem on the half-line

This paper presents a variety of existence results for nonlinear multi-point boundary value problem on the half-line. In particular, we consider

     

Multiple solutions of impulsive boundary value problems on the half-line

Existence results of multiple solutions are obtained under suitable conditions for impulsive integrodifferential boundary value problems on the half-line which may be singular at the boundary.     

Multiple positive solutions of n-point boundary value problems on the half-line in Banach spaces

In this paper, the fixed point index theory is used to investigate the existence of at least two positive solutions of n-point boundary value problem on the half-line in a Banach space. As an application, we give an example to demonstrate our results.     

Twin positive solutions for quasi-linear multi-point boundary value problems

In this paper, we investigate two classes of quasi-linear multi-point boundary value problems with sign-changing nonlinearity. By applications of fixed point index theory, sufficient conditions for the existence of twin positive solutions are established.     

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.     

On the existence of positive solutions for singular boundary value problems on the half-line

On the basis of a special cone and the application of the fixed point theory, some new results for the existence of positive solutions of singular Sturm–Liouville boundary value problems on the half-line are obtained.     

Triple positive solutions for a class of third-order p-Laplacian singular boundary value problems

In this work, we study the existence of triple positive solutions for one-dimensional p-Laplacian singular boundary value problems $$\begin{array}{l}(\phi_p(y''(t)))'+f(t)g(t,\,y(t),\,y'(t),\,y''(t))=0,\quad 0<t<1,\\[3pt]ay(0)-by'(0)=0,\qquad cy(1)+dy'(1)=0,\qquad y''(0)=0,\end{array}$$ where φ _p (s)=|s| ^p?2 s,?p>1, g:[0,?1]×[0,?+∞)×R ²?[0,?+∞) and f:(0,?1)?[0,?+∞) are continuous. The nonlinear term f may be singular at t=0 and/or t=1. Firstly, Green’s function for the associated linear boundary value problem is constructed. Then, by making use of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the above boundary value problem. The interesting point is that the nonlinear term g involved with the first-order and second-order derivatives explicitly.     

一类含导数的 p-Laplacian 方程 m-点边值问题的正解存在性

通过利用 Krasnosel'skii 不动点定理的扩充定理,对于一类含导数的一维p-Laplacian 方程 m-点边值问题建立了至少一个正解的存在性定理,并给出例子加以说明.     

一类含有p-拉普拉斯算子的二阶边值问题的单调迭代正解（英文）

研究了一类含有p-拉普拉斯算子的微分方程积分边值问题.运用迭代技巧,给出了这一类边值问题的单调正解,值得感兴趣的是微分方程中的非线性项含有一阶导数.     

Multiple positive solutions for second-order m-point boundary value problems

In this paper, the second-order m-point boundary value problem

     

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.     

The existence of three positive solutions for some nonlinear boundary value problems on the half-line

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line