Two positive solutions of a boundary value problem for difference equations

We consider a second order vector boundary value problem for difference equations and establish criteria for the existence of at least two positive solutions by an application of a fixed point theorem in cones.     

Multiplicity of positive solutions to period boundary value problems for second order impulsive differential equations

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.     

On the impulsive boundary value problems for nonlinear Hamiltonian systems

In this work, we deal with two‐point boundary value problems for nonlinear impulsive Hamiltonian systems with sub‐linear or linear growth. A theorem based on the Schauder fixed point theorem is established, which gives a result that yields existence of solutions without implications that solutions must be unique. An upper bound for the solution is also established. Examples are given to illustrate the main result. Copyright © 2016 John Wiley & Sons, Ltd.     

Three positive solutions for boundary value problem for differential equation with Riemann-Liouville fractional derivative

In this paper, by using the Avery-Peterson fixed point theorem, we establish the existence result of at least three positive solutions of boundary value problem of nonlinear differential equation with Riemann-Liouville''s fractional order derivative. An example illustrating our main result is given. Our results complements and extends previous work in the area of boundary value problems of nonlinear fractional differential equations.     

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

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

     

含积分边界条件的分数阶微分方程边值问题的正解的存在性

研究了含积分边界条件的分数阶微分方程的边值问题,首先给出格林函数及性质,其次将问题转化为一个等价的积分方程,最后应用Krasnoselkii及Leggett-Williams不动点定理得到了一个及多个正解的存在性,推广了以往的结果．     

Existence of multiple positive solutions for nonlinear m-point boundary value problems

In this paper, we afford some sufficient conditions to guarantee   the existence of multiple positive solutions for the nonlinear m-point boundary value problem for the one-dimensional p-Laplacian

     

Existence of positive solutions for a general nonlinear eigenvalue problem

Let Ω R n be a bounded domain, H = L 2 (Ω), L : D(L) H → H be an unbounded linear operator, f ∈ C(■× R, R) and λ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = λf (x, u), u ∈ D(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a second-order ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.     

On positive solutions for fourth-order boundary value problem with impulse

In this paper, we consider a fourth-order boundary value problem with impulse. First, we establish criteria for the existence of one or more than one positive solution of a non-eigenvalue problem. Second, we are concerned with determining values of λ$\lambda$, for which there exist positive solutions for an eigenvalue problem. In both problems, we shall use the Krasnoselskii fixed point theorem.     

Monotone positive solution for three-point boundary value problem

In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：
x″（t）＋f（t,x（t））=0,0〈t〈1,
x′（0）=0,x（1）＋δx′（η）=0,
where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.     

Multiple positive solutions to third-order three-point singular semipositone boundary value problem

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order threepoint singular semipositone BVP:

Triple positive periodic solutions of nonlinear singular second-order boundary value problems

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″(t) + λ(t)u(t) = f(t,u(t)),a.e.t ∈ [0,2π],u(0) = u(2π),u′(0) = u′(2π),where f(t,u) is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett–Williams and Krasnosel'skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.     

The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions

In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem where 0≤λ < 1,^CD^α is the Caputo's differential operator of order α, and f:[0,1] × [0,∞)→[0,∞) is a continuous function. Using some cone theoretic techniques, we deduce a general existence theorem for this problem. Then, we consider two following more general problems for arbitrary α, 1≤n < α≤n + 1: Problem 1: where , 0≤λ < k + 1; Problem 2: where 0≤λ≤α and D^α is the Riemann–Liouville fractional derivative of order α. For these problems, we give existence results, which improve recent results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

Existence of positive solutions to n-point nonhomogeneous boundary value problem

In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem.     

四阶边值问题的非负解

讨论了一类四阶非线性常微分方程两点边值问题非负解的存在性.利用锥不动点指数理论得到了方程存在非负解的充分条件.