二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

具连续变量和最大值项的二阶差分方程的振动性

研究了一类具有最大值项和连续变量的非线性二阶中立型时滞差分方程的振动性,利用Banach空间的不动点原理和一些不等式技巧,得到了这类方程存在最终正解的充分条件,并得到了该方程振动的一些判别准则.     

具连续变量的二阶非线性差分方程振动和非振动的充要条件

研究了一类具有连续变量的二阶非线性差分方程的振动性质,利用Banach空间的不动点原理和一些分析技巧,得到了这类方程存在非振动解的充分必要条件,并得到了这类方程振动的充分必要条件,同时给出了说明定理应用的例子.     

具正负系数的二阶中立型时滞差分方程的振动和非振动准则

研究了一类具有正负系数的二阶非线性中立型时滞差分方程的振动性,利用Banach空间的不动点原理,结合Riccati变换,获得了该类方程存在非振动解的一些新的准则,并同时得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.     

具有连续变量的差分方程振动性的判据

借助研究离散变量的差分方程振动性的一般方法,本文建立了具有连续变量、变系数的差分方程振动性判据,其结果改进了文献［４］中的一些结果．     

测度链上一类三阶半线性中立型时滞动力方程的振动准则

利用广义Riccati代换及时标上一些分析技巧给出时标上一类三阶半线性动力方程的振动准则,并利用例子说明其结果的可用性,推广了一些已知的二阶或三阶动力方程振动性的结果.     

高阶线性时滞微分方程的广义振动性

该文考虑了一类高阶线性常系数时滞微分方程 y( n) (t) py′(t) qy(t-τ) =0的广义振动性和广义非振动性 ,给出了一些该类方程广义振动和广义非振动的判定定理 .文中的定理 4还给出了一类非振动但广义振动的方程的判别法则     

具有变系数的偶数阶中立型差分方程的振动性

考虑了一类具有变系数的偶数阶中立型差分方程的振动性,通过建立一个比较定理,获得一些一类具有变系数的偶数阶中立型差分方程的振动性的充分条件.     

某些一阶非齐次中立型微分差分方程的振动性

该文讨论了 d/dt[x(t) cx(t-τ)] P(t)x(t-σ) f(t)=0,t≥t_0一阶非齐次中立型微分差分方程的振动性.得到了一些方程振动的充分条件,推广了某些齐次方程的振动结果.     

二阶非线性阻尼方程的振动准则

利用Riccati变换和积分平均方法,研究了一类具有阻尼项的二阶非线性方程的解为振动的若干充分条件,建立了一些判定上述方程为振动的充分准则,结果推广并加强了已有的一些振动准则．     

Oscillatory and asymptotic criteria of third order nonlinear delay dynamic equations with damping term on time scales

In this paper, we are concerned with oscillatory and asymptotic behavior of third order nonlinear delay dynamic equations with damping term on time scales. By using a generalized Riccati function and inequality technique, we establish some new oscillatory and asymptotic criteria. The established results on one hand extend some known results in the literature, on the other hand unify continuous and discrete analysis as two special cases of an arbitrary time scale. We also present some applications for the established results.     

On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces

We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.     

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory.     

Spectral stability results for higher-order operators under perturbations of the domain

We analyze the spectral behavior of higher-order elliptic operators when the domain is perturbed. We provide general spectral stability results for Dirichlet and Neumann boundary conditions. Moreover, we study the bi-harmonic operator with the so-called intermediate boundary conditions. We give special attention to this last case and analyze its behavior when the boundary of the domain has some oscillatory behavior. We will show that there is a critical oscillatory behavior and that the limit problem depends on whether we are above, below or just sitting on this critical value.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates of rough maximal functions along surfaces with applications

In this paper, we study the L^p mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the L^p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(S^n-1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.     

L~p Estimates of Rough Maximal Functions Along Surfaces with Applications

In this paper,we study the L~p mapping properties of certain class of maximal oscillatory singular integral operators.We prove a general theorem for a class of maximal functions along surfaces.As a consequence of such theorem,we establish the L~p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L(S~(n-1)).Moreover,we highlight some additional results concerning operators with kernels in certain block spaces.The results in this paper substantially improve previously known results.     

一类具连续分布滞量的偶数阶非线性中立型方程的振动定理

研究一类具有连续分布滞量的偶数阶非线性中立型泛函微分方程解的振动性,得到了该类方程的若干新的振动准则.所得结果推广和包含了已知的一些结论.     

Oscillatory hyper-Hilbert transform along curves on modulation spaces

We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results.     

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ—TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Hertz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebrasin higher dimensions.     

非线性泛函微分方程解的性态

本文给出了一类非线性泛函微分方程解的性态的若干充要条件,推广了[1]的某些结论.