一类二阶微分方程同宿解的存在性

讨论下列二阶微分方程(y|¨)+ay+U_y(t,y)=0.的同宿解的存在性,其中t∈R,y∈Rⁿ,n∈N,a>0是一个常数,U(t,y)∈Cn,n∈N,a>0是一个常数,U(t,y)∈C¹(R×R1(R×Rⁿ,R),U_y(t,y)表示U(t,y)关于y的梯度.引入快同宿解的概念并给出方程存在快同宿解的判定准则.     

一类时滞Duffing微分方程同宿解的存在性

利用重合度理论和一些分析技巧,得到一类二阶时滞Duffing微分方程的2kT周期解,通过对该微分方程的一系列周期解取极限获得同宿解的存在性.同时,β(t)是可变号的.     

一类具有变号位势的超二次Kirchhoff方程解的多重性

本文研究一类全空间上的Kirchhoff型方程.当非线性项是凹凸混合项且f在无穷远处满足超二次增长时,利用变分方法获得方程解的多重性结果,改进和推广了相关文献中的结论.     

具有退化三次曲线解的Hamilton二次系统的Poincare分支

具有退化三次曲线解的Hamilton二次系统,经二次微扰后的Poincare分支,是否存在两个极限环?这是一个长期受到困扰的问题.本文证明了在特定条件下,可以分支出两个极限环.     

一类二阶渐近周期Hamilton系统同宿轨道

运用变分方法讨论二阶渐近周期Hamilton系统 -u+L(t)u=(1+g(t))V′(t,u)的Lagrange泛函在流形上的极小问题,进而证明该系统存在非平凡同宿轨道,其中L,V关于t是周期的,g(t)→0(|t|→∞).     

同宿环的环性数和退化三次Hamilton函数 *

对多参数扰动下的平面同宿环给出了环性数为2的新条件 .作为应用 ,证明了非通有二次Hamilton系统的同宿环在任意二次扰动下具有环性数2 .     

一类非线性离散系统的同宿解的存在性

应用临界点理论讨论一类二阶非线性离散系统在一定条件下非零同宿解的存在性,得到一个非零同宿解存在性的条件.     

一类二阶Hamilton系统的周期解

本文研究一类含非定线性项的二阶Ｈａｍｉｌｔｏｎ系统多周期解问题．在位势函数满足超二次齐次条件下，利用临界点理论中对称型越山定理，证明了系统存在无穷多个给定周期的周期解．     

一类特殊二次规划最优解的性质

本文研究了一类特殊二次规划最优解的性质.利用凸分析的方法,得到了该类二次规划问题解的存在性,唯一性及其结构.文中结果推广了模松弛QP子问题的有关结论,并在更多的QP子问题中有着潜在的应用.     

Homoclinic Solutions for a Class of Second Order Hamiltonian Systems

In this paper we consider the existence of homoclinic solutions for the following second order non-autonomous Hamiltonian system $${\ddot q}-L(t)q+\nabla W(t,q)=0, \quad\quad\quad\quad\quad\quad\quad (\rm HS)$$ where ${L\in C({\mathbb R},{\mathbb R}^{n^2})}$ is a symmetric and positive definite matrix for all ${t\in {\mathbb R}}$ , W(t, q)?=?a(t)U(q) with ${a\in C({\mathbb R},{\mathbb R}^+)}$ and ${U\in C^1({\mathbb R}^n,{\mathbb R})}$ . The novelty of this paper is that, assuming L is bounded from below in the sense that there is a constant M?>?0 such that (L(t)q, q)?≥ M |q|² for all ${(t,q)\in {\mathbb R}\times {\mathbb R}^n}$ , we establish one new compact embedding theorem. Subsequently, supposing that U satisfies the global Ambrosetti–Rabinowitz condition, we obtain a new criterion to guarantee that (HS) has one nontrivial homoclinic solution using the Mountain Pass Theorem, moreover, if U is even, then (HS) has infinitely many distinct homoclinic solutions. Recent results from the literature are generalized and significantly improved.     

Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems

The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)), where H(t, z) =1/2(B(t)z, z) +H(t, z),B(t) is a semipositive symmetric continuous matrix andH is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a_j T-periodic nonconstant brake solution z_j such that z_j and z_(kj) are distinct.     

Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

In this paper, we discuss the existence and multiplicity of homoclinic solutions for fractional Hamiltonian systems with left and right Liouville–Weyl fractional derivatives. Sufficient conditions ensuring the existence of an unbounded sequence of homoclinic solutions for the given problem are obtained via variational approach.     

Multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems with Local Conditions at the Origin

In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systems ü(t)-L(t)u(t)+▽_uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L ∈C(R,R^N×N) is symmetric but non-periodic,W ∈C¹(R×R^N,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.     

具有次二次双偶位势的二阶哈密顿系统多重非平凡奇周期解的存在性

利用变分理论中的Clark定理,讨论了一类具有次二次双偶位势的二阶哈密顿系统(x|¨)(t)+V_x(t,x(t))=0多重非平凡奇周期解的存在性.     

一类次二次二阶哈密尔顿系统的周期解的存在性

运用临界点理论中的极小极大方法,得到了一类次二次位势条件和半强制条件下的二阶哈密尔顿系统的周期解的存在性,改进了某些已有的结果.     

一类Hamilton系统的同宿解存在性

We study the existence of homoclinic orbits for some Hamiltonian system.A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a sequence of systems of differential equations.     

Multiple Homoclinic Solutions for Second‐Order Perturbed Hamiltonian Systems

In this paper, we study the second‐order perturbed Hamiltonian systems where is a parameter, is positive definite for all but unnecessarily uniformly positive definite for , and W is either asymptotically quadratic or superquadratic in x as . Based on variational methods, we prove the existence of at least two nontrivial homoclinic solutions for the above system when small enough.     

Homoclinic Solutions for A Class of Second Order Neutral Functional Differential Systems

By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.