POSITIVE SOLUTIONS TO m-POINT BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH p-LAPLACIAN

In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.     

一维P-Laplacian方程正解的三解定理

本文应用Leggett-Williams不动点定理,研究具有P-Laplacian算子的非线性边值问题(φ(u′))′+α(t)f(u)=0,αφ(u(0))-βφ(u′(0))=0,γφ(u(1))+δφ(u′(1)) =0正解的存在性,其中φ(s):=|s|~(p-2)s,p>1,我们建立了该问题至少存在三个正解的充分条件。     

EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM

We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive solutions are established.     

MULTIPLE SOLUTIONS TO A SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM

In this paper, we are concerned a class of second-order m-point boundary value problem. The existence results of at least three positive solutions are given by using a fixed-point theorem and imposing growth conditions on the nonlinear term, which depends on the first derivative.     

EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type, we establish results on the existence of at least one, at least two, and $n$ positive solutions to the boundary value problem. Finally we give an example.     

POSITIVE SOLUTIONS TO AN INTEGRAL BOUNDARY VALUE PROBLEM WITH DELAY

In this paper, we study a second order integral boundary value problem with delay. By the Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions to the problem.     

测度链上非线性微分方程的三正解

运用文[1]中的Leggett—Williams不动点定理，我们给出了测度链上的非线性微分方程-x^△△(t)=f(t,x(σ(t))),t∈[a,b,]关于两点边值条件ax(a)-βx^△(a)=0，γx(σ(b)) δx^△(σ(b))=0三正解存在性准则。     

MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.     

EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM

In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.     

POSITIVE SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEM FOR NONLINEAR RETARDED DIFFERENTIAL EQUATION

§1　IntroductionAt present,boundary value problems (BVPs) are widely investigated with variousmethods and techniques. BVPs with integral boundary conditions constitute a veryinteresting class of problems such as multipoint,three-point,four-point and nonlocalboundary value problems which are considered by many authors.And the existence ofpositive solutions for these problems becomes the subjectof many papers[1—6] .In a recentpaper[7] ,the authors have studied the existence of positive solut…     

POSITIVE SOLUTIONS TO FOURTH ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN OPERATOR

In this paper, we consider the existence of positive solutions to a singular fourth order p-Laplacian equation. By the upper and lower solution method and fixed point theorems, the existence of positive solutions to the boundary value problem is obtained under the assumption that the nonlinear term is decreasing.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.     

POSITIVE SOLUTIONS TO SECOND-ORDER SINGULAR NEUMANN BOUNDARY VALUE PROBLEM WITH PARAMETERS IN THE BOUNDARY CONDITIONS

In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.     

一类四阶奇异边值问题对称正解的最优存在性

本文研究了一类四阶奇异边值问题.通过建立一个特定的锥,利用Leggett-Williams不动点定理,从而在一定的条件下得到一类四阶奇异边值问题对称正解的最优存在性,推广了奇异边值问题对称正解的最优存在性的结果.     

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η∈ (0, 1), α∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ∈ (0, λ*) under certain conditions on the nonlinear term f.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETER

In this paper, we consider a class of nonlinear fractional differential equation boun- dary value problem with a parameter. By some fixed point theorems, sufficient con- ditions for the existence, nonexistence and multiplicity of positive solutions to the system are obtained. An example is given to illustrate the main results.     

带非齐次边界条件的奇异边值问题的正解

本文讨论奇异边值问题的正解存在性,其中q(t),(t,y)≥0并且q可能在t=0附近,f可能在y=0附近具有奇异性.     

EXISTENCE OF AT LEAST THREE POSITIVE SOLUTIONS TO MULTI-POINT BOUNDARY VALUE PROBLEM WITH p-LAPLACIAN OPERATOR

In this paper,we consider a multi-point boundary value problem. We obtain suffcient conditions ensuring the existence of at least three positive solutions to the boundary value problem.     

MULTIPLE POSITIVE SOLUTIONS OF A CLASS OF THREE-POINT SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence theorem for three positive solutions is presented for the singular nonlinear boundary value problem by applying the extended Five Functionals fixed point theorem. singular nonlinear boundary value problem; positive solutions; cone; fixed point theorem     

TWIN POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR SECOND-ORDER THREE-POINTS BOUNDARY VALUE PROBLEMS

In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions.