一类超线性不对称Duffing方程的Aubry-Mather集

通过引进合适的作用-角变量变换,并运用新的估计方法,对超线性不对称Duffing方程的Poincaré映射,应用推广的Aubry-Mather定理,证明了一类超线性不对称Duffing方程的Aubry-Mather集的存在性.     

一类超线性Duffing方程的Aubry-Mather集

本文通过引进适当的作用-角变量变换并结合新的估计方法,对超线性Duffing方程的Poincaré映射应用推广的Aubry-Mather定理,获得了一类超线性Duffing方程的Aubry-Mather集存在的充分性条件.     

次线性不对称Duffing 方程的Aubry-Mather 集

本文通过引进合适的作用— 角变量变换并结合新的估计方法, 对次线性不对称Duffing 方程的Poincaré 映射应用推广的Aubry-Mather 定理, 获得了一类次线性不对称Duffing 方程的Aubry-Mather 集存在的充分性条件.     

一类含Hardy-Leray势的分数阶p-Laplacian方程解的单调性和对称性

本文研究在有界域和无界域上含Hardy-Leray势的分数阶p-Laplacian方程,运用移动平面法,得到该方程正解的单调性和对称性,并将带Hardy-Leray势的分数阶方程解的对称性结果推广到更一般的分数阶p-Laplacian方程.     

一类具有p-Laplacian算子的分数阶差分方程边值问题的正解

该文研究一类具有p-Laplacian算子的分数阶差分方程边值问题.借助离散型Jensen不等式,考虑该问题与相应的不带有p-Laplacian算子的分数阶差分方程边值问题之间的关系,并运用不动点指数理论获得该问题正解的存在性.     

分数阶p-Laplacian Kirchhoff型问题正解的存在性

研究了分数阶p-Laplacian Kirchhoff方程,运用变分法和截断函数理论,证明了在一定条件下具有消失Kirchhoff项的分数阶p-Laplacian问题正解的存在性和多重性.     

一类可逆系统的Aubry-Mather集

本文利用推广的Aubry-Mather定理,获得了一类二阶可逆微分方程Aubry-Mather集存在的充分性条件.     

一类p-Laplacian型Neumann边值问题非平凡解的存在性及迭代算法研究

首先将一类p-Laplacian型Neumann边值问题转化为含有极大单调算子的算子方程的形式,得到算子方程解的存在性结论,进而证明p-Laplacian型Neumann边值问题有非平凡解;其次,借助于极大单调算子的相对预解式构造出强收敛到极大单调算子零点的迭代序列;最后,建立p-Laplacian型Neumann边值问题的解与极大单调算子零点的关系,得到解的迭代逼近序列.推广和补充了以往的相关研究成果.     

一类次线性p-Laplacian椭圆方程的多重正解

利用极小化作用原理和山路引理,可证明一类次线性p-Laplacian椭圆方程多重正解的存在性.     

带不定权非线性边界的p-Laplacian问题解的存在性

研究了一类带不定权非线性边界的p-Laplacian椭圆方程.获得了当非线性边界的特征值参数小于第二特征值时,该方程存在非平凡解.主要工具为环绕定理.     

The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations

We investigate the large-time behavior of viscosity solutions of the Cauchy-Dirichlet problem (CD) for Hamilton-Jacobi equations on bounded domains. We establish general convergence results for viscosity solutions of (CD) by using the Aubry-Mather theory.      

MATHER SETS FOR SUBLINEAR DUFFING EQUATIONS

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Hamilton-Jacobi methods for Vakonomic Mechanics

We extend the theory of Aubry-Mather measures to Hamiltonian systems that arise in vakonomic mechanics and sub-Riemannian geometry. We use these measures to study the asymptotic behavior of (vakonomic) action-minimizing curves, and prove a bootstrapping result to study the partial regularity of solutions of convex, but not strictly convex, Hamilton-Jacobi equations.      

含有一阶导数的一维p-Laplace方程的正解

通过利用积分方程全连续算子的不动点指数对含有一阶导数的一维p-L ap lace方程建立了一个存在定理.这个定理表明此p-L ap lace方程必有一个正解,只要非线性项在某个有界集合上的“最大高度”是适当的.     

Asymptotic behavior of the solutions of the p-Laplacian equation

The asymptotic behavior of the solutions for p-Laplacian equations as p→∞ is studied.     

Positive Radial Solutions of Some Nonlinear Partial Differential Equations

We consider Dirichlet boundary value problems for a class of nonlinear ordinary differential equations motivated by the study of radial solutions of equations which are perturbations of the p-Laplacian.     

Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources

This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and themethod of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.     

Minimization of eigenvalues and construction of non-degenerate potentials for the one-dimensional p-Laplacian

We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of nondegenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations.