依赖于一阶导数的(n-1,1)共轭m点边值问题正解的存在性

利用锥上的Krasnoselskii's不动点定理的推广定理,讨论了一类边值问题,给出了相应依赖于一阶导数的非线性n阶m点边值问题至少一个正解的存在性.对于n阶m点边值问题,给出了相应的Green 函数.证明了在非线性项厂满足一定的增长条件下至少存在1个正解.并且给出了一个例子来说明所获得的结果.     

一类次线性分数微分方程的正解存在性

证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性.主要方法是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用.我们的结论表明该方程可以具有一个正解,只要非线性项在某个有界集上的“高度”是适当的.     

一般Lidstone边值问题的n个正解的存在性

考察了含所有偶数阶导数的一般Lidstone边值问题的正解和对称正解.通过 选择合适的Banach空间和锥,对该问题建立了n个正解或者对称正解的存在性,其 中n是一个任意的自然数.基本工具是等价范数和锥拉伸与锥压缩型的Krasnosel'skii 不动点定理. 结论的主要条件是局部的.换言之,如果非线性项f在某些有界集上的 "高度"是适当的,则该问题可以具有n个正解.     

一类非线性二阶常微分方程的正周期解

考察非线性二阶常微分方程u″(t)=,(t,u(t))关于周期边界条件u(0)=u(2π),u′(0)=u′(2π)的正解,由于该方程没有Green函数,通常的方法是无效的.利用适当的转换技巧和锥上的不动点定理证明了这个周期边值问题的n个正解的存在性,其中n是一个任意的自然数.     

一类二阶三点边值问题的解和多解性

利用锥拉伸与锥压缩型Krasnosel'skii不动点定理,给出了一类非线性二阶三点边值问题解和多解的存在性定理,其中允许非线性项有一个负的下界,本文的结论表明该方程可以具有n个解和正解,从而推广和改进了已有的解的存在性的结论.     

二阶带时标的非线性奇异动力方程的m点边值问题的正解

研究二阶带时标的非线性奇异动力方程m点边值问题的正解,利用锥上的混合单调不动点定理,得到了正解的存在性和唯一性.本文中方程的非线性项可能是奇异的.并举例说明相应的结果.     

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.     

半正定差分方程正解的存在性

利用锥压缩与锥拉伸不动点定理,在非线性项具有负下界和非减性条件下,讨论了一类二阶半正定非线性差分方程正解的存在性,改进和推广了现有差分方程的一些结果,并将所获得的结果应用于一个具体的二阶半正定非线性差分方程中.     

一类含参数半正四阶边值问题的正解存在性与多解性

考察了一类含有两个参数的非线性四阶边值问题的n个解和/或正解的存在性,其中允许非线性项有一个非正的函数型下界.在力学和工程上,这类四阶边值问题描述了两端简单支撑的弹性梁的变形.主要工具是锥上的Krasnosel’skii不动点定理和局部化方法.     

一类含时间奇异性的二阶非线性Dirichlet问题的正解

通过使用Hammastein积分方程和锥上的不动点定理对于一类含时间奇异性的二阶非线性Dirich．1et问题建立了三个局部存在定理．主要结论表明只要非线性项的主要部分在某些有界集合上的高度是适当的此问题具有n个正解,其中竹是一个任意的自然数．     

Positive solutions of nonlinear beam equations with time and space singularities

We consider the existence and multiplicity of positive solutions to a nonlinear fourth-order two-point boundary value problem. The nonlinear term may be singular with respect to both the time and space variables. In mechanics, the problem describes the deformation of an elastic beam fixed at the left and supported at the right by sliding clamps. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several local existence theorems are obtained.     

POSITIVE SOLUTIONS TO A SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM ON TIME SCALES

By a fixed point theorem in a cone,the existence of at least three positive solutions to a class of second-order multi-point boundary value problem for dynamic equation on time scales with the nonlinear term depends on the first order derivative is studied.     

Triple positive solutions for boundary value problems on infinite intervals

This paper deals with the existence of triple positive solutions for Sturm–Liouville boundary value problems of second-order nonlinear differential equation on a half line. By using a fixed point theorem in a cone due to Avery–Peterson, we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term.     

非线性四阶周期边值问题正解的存在性和多重性

研究了四阶两参数常微分方程周期边值问题{u（4）（t）-βu″（t）＋αu（t）=f（t,u（τ（t）））,t∈[0,1],u（i）（0）=u（i）（1）,i=1,2,3正解的存在性、多重性和不存在性.在非线性项f（t,u）变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问...     

Positive periodic solution for second-order nonlinear differential equation with singularity of attractive type

This paper is devoted to investigate the following second-order nonlinear differential equation with singularity of attractive type $$ x''-a(t)x=f(t,x)+e(t), $$ where the nonlinear term $f$ has a singularity at the origin. By using the Green''s function of the linear differential equation with constant coefficient and Schauder''s fixed point theorem, we establish some existence results of positive periodic solutions.     

Highly accurate algorithms endowing with boundary functions for solving a nonlinear beam equation involving an integral term

In this paper, the problem of a nonlinear beam equation involving an integral term of the deformation energy, which is unknown before the solution, under different boundary conditions with simply supported, 2‐end fixed, and cantilevered is investigated. We transform the governing equation into an integral equation and then solve it by using the sinusoidal functions, which are chosen both as the test functions and the bases of numerical solution. Because of the orthogonality of the sinusoidal functions, we can find the expansion coefficients of the numerical solution that are given in closed form by using the Drazin inversion formula. Furthermore, we introduce the concept of fourth‐order and fifth‐order boundary functions in the solution bases, which can greatly raise the accuracy over 4 orders than that using the partial boundary functions. The iterative algorithms converge very fast to find the highly accurate numerical solutions of the nonlinear beam equation, which are confirmed by 6 numerical examples.