一类四阶奇摄动非线性边值问题(英文)

This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y（4） =f（t,y＇,y＇＇,y＇＇＇）,0t1,0ε1 with the nonlinear boundary conditions y（0）=y＇（1）=0,p（y＇＇（0）,y＇＇＇（0））=0,q（y＇＇（1）,y＇＇＇（1））=0 where f：[0,1]×R3→R is continuous,p,q：R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.     

EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

We study the existence of solutions to the following parabolic equation{ut-△pu=λ/|x|s|u|q-2u,(x,t)∈Ω×(0,∞),u(x,0)=f(x),x∈Ω,u(x,t)=0,(x,t)∈Ω×(0,∞),(P)}where-△pu ≡-div(|▽u|p-2▽u),1相似文献   

一类奇异三阶三点边值问题的正解

In this paper,we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problemu （t） = λa（t）f（t,u（t））,u（0） = u （1） = u （η） = 0,where λ is a positive parameter and 0 ≤ η 1 2 .By using the classical Krasnosel’skii’s fixed point theorem in cone,we obtain various new results on the existence of positive solution,and the solution is strictly increasing.Finally we give an example.     

非线性奇异二阶三点边值问题的对称正解(英文)

In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 t 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0t1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.     

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 SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.     

THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

In this paper,we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations ut u=g(u)+λf(x),(x,t)×(0,T),u=0,(x,t)∈×[0,T),u(x,0)=u0(x)≥0,x ∈.(P) By combining a priori estimate of global solution with property of stationary solution set of problem(P),we prove that the minimal stationary solution Uλ(x)of problem(P)is stable,whereas,any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem(P).     

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.     

一类高阶非线性微分方程解的存在问题(英文)

This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 0 and c～2+d～20,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.     

具有p-Laplacian算子的奇异四阶积分边值问题的正解

In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.     

左端刚性固定右端简单支撑的奇异梁方程正解的存在性

设E[0,1]是一个零测度的闭子集。对于左端刚性固定右端简单支撑的非线性梁方程u^（（4））（t）=f（t,u（t））,t∈[0,1]／E,u（0）=u（1）=u′（0）=u″（1）=0,证明了一个新的正解存在定理,其中允许非线性项f（t,u）是非单调的并且在t=0,t=1及u=0处是奇异的.主要工具是全连续算子的逼近定理和锥压缩锥拉伸型的Guo-Krasnoselskii不动点原理。     

含各阶导数的非线性弹性梁方程的一个存在定理

通过选择适当的Banach空间并利用Leray-Schauder非线性抉择对于含各阶导数的非线性弹性梁方程{u(4)(t)=f(t,u(t),u′(t),u″(t),u′″(t)),0≤t≤1, u(0)=u′(1)=u″(0)=u′″(1)=0.建立了一个解的存在定理．在材料力学中，该方程描述了一端简单支撑，另一端被滑动夹子夹住的弹性梁的形变．这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解．     

一类含隅角和弯矩的奇异梁方程三个正解的存在性

利用格林函数方法和Avery-Peterson不动点定理研究了一类非线性四阶两点边值问题u(4)(t) =f(t,u(t),u′(t),u″(t)), 0 ＜ t ＜ 1,u(0) =u′(1) =u″(0) =u′″(1) =0多个正解的存在性,其中允许非线性项f(t,u,v,w)在t=0,t=1,u=0,v=0,w=0处奇异.在力学上该问题模拟了左端简单支撑右端被滑动夹子夹住的弹性梁的挠曲.由于非线性项同时涉及隅角和弯矩,因此主要结论对于梁的稳定性分析是有益的.最后我们给出了一个例子,进一步证实本文理论的严密性和可行性.     

弱半正三阶三点边值问题的正解

The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈[0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f（t, u） 〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.     

缺乏单调性的奇异三阶三点边值问题的正解(英文)

考虑了非线性三阶三点边值问题u′′′(t)=f(t,u(t))+g(t,u(t)),0t1,u(0)=u′(η)=u′′(1)=0的正解.本文中g(t,u)可以在t=0,t=1及u=0处奇异,而且允许g(t,u)关于u不是非减的.通过构造适当的控制函数并且利用锥上的Guo-Krasnoselskii不动点定理,证明了若干新的局部存在定理.     

一维奇异p-Laplacian方程多解的存在性

该文通过利用Leggett-Williams定理,建立了一维奇异p-Laplacian非线性边值问题(\varphi(u'))'+a(t)f(u)=0,\u'(0)=u(1)=0 (或者u(0)=u'(1)=0),其中\varphi(s)=|s|^{p-2}s, p>1三解的存在性定理,推广并丰富了以往文献的一些结论.     

一类非线性悬臂梁方程正解的存在性与多解性

研究了非线性四阶常微分方程u(4)(t)=f(t,u(t),u'(t)),t ∈[0,1]\E在边界条件u(0)=u'(0)=u"(1)=u"'(1)=0下的正解,其中E(∩)[0,1]是一个零测度的闭集,而非线性项,(t,u,u)可以在t∈E时奇异.通过构造适当的积分方程并利用锥上的不动点定理证明了这个方程在满足与n有关的条件下存在n个正解,其中n是某个自然数.     

二阶三点半正边值问题正解的存在性

利用锥的Krasnosel'skill不动点定理建立了二阶三点半正边值问题u″+λf(t,u)+δg(t,u)=0, t∈(0,1),u(0)=0, αu(η)=u(1).其中,λ,δ＞0, 0＜η＜1, 0＜αη＜1正解的存在性,这里,非线性项不需要是非负的.     

带p-Laplacian算子的四点边值问题拟对称正解的存在性

利用范数形式的锥拉伸与压缩不动点定理,研究了一类p-Laplacian方程四点边值问题(φp(u′(t)))′(t)+λf(t,u(t))=0,t∈(0,1),u(0)-βu′(ξ)=0,u(ξ)-δu′(η)=u(1)+δu′(1+ξ-η),其中φp(s)=sp-2·s,p>1.获得了其拟对称正解的存在性定理.     

四阶奇异边值问题的正解

研究了一类四阶奇异边值问题正解的存在性,在f和g满足比超线性和次线性条件更广泛的极限条件下,利用锥压缩和拉伸不动点定理获得了正解的存在性结果,推广和包含了一些已知结果.