由p(x)-Laplace算子导出的不等式Dirichlet问题的三解

讨论了一类具有非光滑位势的p(x)-Laplace非线性椭圆问题.利用非光滑的三临界点定理证明了该问题在变指数Sobolev空间W01,p(x)(Ω)中至少存在3个非平凡解.     

含p(x)-Laplacian算子的Neumann问题解的存在性

利用极大单调算子理论,给出了一类含p(x)-Laplacian算子的Neumann边值问题解的存在的充分条件.讨论用到了Lp(x)(Ω)和W01,p(x)(Ω)空间的理论.     

广义(PS)条件的证明

在广义Lebesgue空间Lp~(x)(Ω)和广义Sobolev空间W~(1,p(x))(Ω)的基本理论体系的基础上得到了一类p(x)-Laplace方程满足广义(PS)条件的一个充分条件.     

一类Kirchhoff型p(t)-Laplace系统的无穷多周期解北大核心CSCD

利用变指数Sobolev空间理论和临界点理论,研究Kirchhoff型p(t)-Laplace系统的周期解.当非线性项在零点附近次线性或在无穷远处超线性增长时,得到了此类系统无穷多个周期解的存在性.     

一类Kirchhoff型p(t)-Laplace系统的无穷多周期解

利用变指数Sobolev空间理论和临界点理论,研究Kirchhoff型p(t)-Laplace系统的周期解.当非线性项在零点附近次线性或在无穷远处超线性增长时,得到了此类系统无穷多个周期解的存在性.     

类p(x)-Laplace方程解的存在性

应用变分法且以临界点理论为工具,利用山路引理,借助广义Lebesgue空间和广义Sobolev空间的基本理论,尤其是嵌入定理,H■lder不等式及Egorov定理获得了当非线性项满足超线性增长条件时,类p(x)-Laplace方程解的存在性.     

Bochner可积空间L~p(μ,X)的左右极限空间

定义了Bochner可积空间L~p(μ,X)的左极限空间L~(p-0)(μ,X)和右极限空间L~(p+0)(μ,X).得到了L~(p-0)(μ,X)是完备的完全仿范空间,L~(p+0)(μ,X)是包囿空间和桶空间.并在最后给出关于L~p(μ,X),L~(p-0)(μ,X)和L~(p+0)(μ,X)的连续嵌入定理.     

广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性

本文研究了广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性.利用对函数进行环形分解技术和算子截断的方法,获得了广义分数次积分算子L~(-β/2)(f)从MK_(p,q1)~(α,λ)(ω1,ω_2~(q1))空间到MK_(p,q2)~(α,λ)(ω_1,ω_2~(q2))空间是有界的,从而将分数次积分算子在齐次加权Morrey-Herz空间上的有界性推广到广义分数次积分算子.     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

广义Heronian平均与幂平均的最优比较

比较了含有两个参数的广义Heronian平均H_(p,W)(a,b)与幂平均M_q(a,b)的大小,得到了M_q(a,b)≥(≤)H_(p,w)(a,b)对于任意a,b>0成立的充要条件.     

广义非线性变分包含的带误差的近似点算法

引入和研究了一类新的广义非线性变分包含．在Hilbert空间中利用与极大η-单调映象相联系的预解算子的性质，对新的广义非线性变分包含建立了一个新的寻求近似解的带误差的近似点算法，并证明了求近似解序列强收敛于精确解．其所得结果是近期相关结果的改进和推广．     

On general over-relaxed proximal point algorithm and applications

A general framework to the over-relaxed proximal point algorithm based on H-maximal monotonicity is introduced, and then it is applied to the approximation solvability of a general class of nonlinear inclusion problems based on the generalized resolvent operator technique. This form of the proximal point algorithm seems to be more application-oriented to inclusion problems.     

Convergence of over-relaxed contraction-proximal point algorithm in Hilbert spaces

The proximal point algorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and Xu proposed two modifications of the PPA and established strong convergence theorems on these two algorithms. However, these two convergence theorems exclude an important case, namely, the over-relaxed case. In this paper, we extend the above convergence theorems from under-relaxed case to the over-relaxed case, which in turn improve the performance of these two algorithms. Preliminary numerical experiments show that the algorithm with over-relaxed parameter performs better than that with under-relaxed parameter.     

Relatively maximal monotone mappings and applications to general inclusions

Based on the relative maximal monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems is explored, while generalizing most of the investigations on weak convergence using the proximal point algorithm in a real Hilbert space setting. Furthermore, the main result has been applied to the context of the relative maximal relaxed monotonicity frameworks for solving a general class of variational inclusion problems. It seems that the obtained results can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions, and the obtained results can further be applied to the Douglas–Rachford splitting method for finding the zero of the sum of two relatively monotone mappings as well.     

带有模糊集值映象的一般混合拟变分包含的扰动近似点算法

本文引入一类新的带有模糊集值映象的一般混合拟变分包.在Hilbert空间中,利用极大η-单调映象的预解算子技巧,建立了这类变分包与不动点的等价性.利用这种等价性,构造了一些新的扰动近似点算法,并证明了由此算法所产生的迭代序列的收敛性.这些定理改进,统一和推广了近期文献中许多重要结果.     

New approach to the η-proximal point algorithm and nonlinear variational inclusion problems

A new approach using the over-relaxed proximal point algorithm in the context of solving a class of inclusion problems based on the notion of maximal (η)-monotonicity is developed and examined. Convergence analysis seems to be reasonable, and finally, some specializations are included. Furthermore, the model developed in this communication seems to be appropriate to the Yosida approximation in the sense that it can be applied to first-order evolution equations/inclusions as well.     

对带误差项的Banach空间中完全广义集值拟变分包含的摄动迭代算法

研究了一类新的实Banach空间中的广义集值拟变分包含:f∈N(x，y) M(z，v) W(g(u)-h(w)，u)，它包含了近几年许多作者所作的变分包含同题．在买Banach空间中，利用极大增生算子的性质，建立了Banach空间中的广义集值拟变分包含和不动点问题间的等价性．利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果。     

A New System of Generalized Variational Inclusions Involving $H$-$η$-Monotone Operators in Uniformly Smooth Banach Spaces

In this paper, we introduce and study a new system of generalized variational inclusions involving $H$-$η$-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with $H$-$η$-monotone operators, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.     

Banach空间一类H-增生算子的混合拟变分包含的邻近算子方程

本文在Banach空间中引入一类H-增生算子的混合拟变分包含,并提出求该变分包含问题解的邻近点法.通过H-增生算子的预解算子技术,建立了混合拟变分包含问题与邻近算子方程的等价关系,由这个等价关系得到求解邻近算子方程的迭代算法,该算法收敛于上述混合拟变分包含问题的解.     

Banach空间中的广义Hη增生算子及其在变分包含中的应用

在Banach空间中,引入和研究了新的广义H-η-增生算子,对广义m-增生算子与H-η-单调算子提供了一个统一的框架．还定义了广义H-η-增生算子相应的预解算子,并且证明了其Lipschitz连续性．作为应用,考虑了涉及广义H-η-增生算子的一类变分包含问题的可解性．利用预解算子方法,构造了一个求解变分包含的迭代算法．在适当假设下,证明了变分包含解的存在性和由算法生成的迭代序列的收敛性．