非线性三阶微分方程组边值问题的多个正解

本文通过利用范数形式的锥拉伸和压缩不动点定理及Leggett-Williams不动点定理,获得了非线性三阶微分方程组边值问题多个正解的存在性,并给出了一些例子说明结果的应用.     

Existence and Numerical Solutions of Nonlinear Quadratic Integral Equations Defined on Unbounded Intervals

The first goal of this article is to discuss the existence of solutions of nonlinear quadratic integral equations. These equations are considered in the Banach space L ^p (?₊). The arguments used in the existence proofs are based on Schauder's and Darbo's fixed point theorems. In particular, to apply Schauder's fixed point theorem based method, a special care is devoted to the proof of the L ^p -compactness of the operators associated with our nonlinear quadratic integral equations. The second goal of this work is to study a numerical method for solving nonlinear Volterra integral equations of a fairly general type. Finally, we provide the reader with some examples that illustrate the different results of this work.     

Positive solutions of a singular nonlinear third order two-point boundary value problem

In this paper some existence results of positive solutions for the following singular nonlinear third order two-point boundary value problem:

     

具有p-Laplacian算子的二阶微分方程Picard边值问题(英文)

Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ（x（t））] ＋ kx（t） ＋ g（t,x（t）） = p（t）,t ∈（0,π） x（0） = x（π） = 0 are established,where [φ（x）] =（｜x ｜p-2x） with p 1.Our result is new even when [φ（x）] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.     

一类分数阶微分方程边值问题正解的存在性

构建了一格林函数,采用新的分析方法即利用锥拉伸锥压缩不动点定理和Leggett—Williams不动点定理,在较弱的条件下研究了一类分数阶微分方程,得到该问题一个以及多个正解的存在性,使原有结果得到进一步改进,并给出了一个实例．     

EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.     

Two-Point Boundary Value Problems for Duffing Equations across Resonance

In this paper, we consider the equation y″+f(x,y)=0 with a nonresonance condition of the form A≤f _y (x,y)≤B, where (k−1)²<A≤k ²<⋅⋅⋅<m ²≤B<(m+1)², k,m∈ℤ⁺. With optimal control theory and the Schauder fixed-point theorem, by introducing a new cost functional, we obtain a new existence and uniqueness result for the above equation with two-point boundary-value conditions. This work was supported by NSFC Grant 10501017 and 985 Project of Jilin University.     

一类具p-Laplacian算子方程三个拟对称正解的存在性

研究边值问题(φp(u′))′+q(t)f(t,u,u′)=0,0相似文献   

TRIPLE SYMMETRIC POSITIVE SOLUTIONS TO NONLINEAR BVP WITH INTEGRAL BOUNDARY VALUE CONDITIONS

In the paper,we consider a nonlinear boundary value problem with integral boundary value conditions.By a generalization of the Leggett-Williams fixed-point theorem,we provide sufficient conditions for the existence of at least three positive solutions to the problem.An example is introduced to demonstrate our result.     

Existence and Non-existence of Positive Solutions for a Discrete Fractional Boundary Value Problem

In this work, we deal with two-point boundary problem for a finite nabla fractional difference equation. First, we establish an associated Green''s function and state some of its properties. Under suitable conditions, we deduce the existence and non-existence of positive solutions to the considered problem. Finally, we construct a few examples to illustrate the established results.