高阶非线性差分方程的全局吸引性

研究了一类高阶非线性差分方程所有正解的周期性,不变区间及全局吸引性.证明了方程的正平衡点是在一个依赖于参数的盆里的全局吸引子.     

KD-拉回吸引的非自治动力系统拉回吸引子的存在性及其应用

利用拉回吸引子的存在性理论,证明了具有KD-拉回吸引的非自治动力系统拉回吸引子的存在性,拉回吸引子是单点集,是不变的.对无解域上的非自治反映扩散方程,证明了拉回指数吸引子的存在性,是方程唯一拉回指数吸引的稳定解.     

非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性

非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性王向荣，冯滨鲁，韩茂安（山东矿业学院数学系泰安２７１０１９）关键词：全局吸引性；极限环；存在性ＡＭＳ（１９９１）主题分类：３４Ｃ０５．考虑系统假设ｈ，Ｆ，ｇ均连续且满足解的存在唯一性条件，且...     

弱D-拉回指数吸引子的存在性

主要研究弱D-拉回指数吸引子的存在性.首先讨论了弱D-拉回指数吸引子与非紧性测度之间的关系,其次,建立了弱D-拉回指数吸引子存在性的一般方法,最后证明了外力项具有指数增长速度的反应扩散方程在H_0~1(Ω)中存在弱D-拉回指数吸引子.     

马尔可夫调制的随机时滞微分方程的吸引性

利用It(o)公式和局部鞅收敛定理,确立了马尔可夫调制的随机时滞微分方程吸引性的充分条件;通过适当将条件加强,从而得到了方程更好的吸引性.同时为有界性和稳定性的新准则的确立奠定了基础.     

吊桥方程指数吸引子的存在性

吊桥方程是工程数学中的一类重要数学模型.在非自治和自治两种情况下,吊桥方程紧整体吸引子的存在性已有许多结果.然而,这一问题指数吸引子的存在性还无人讨论.我们借助Eden等人提出的方法,证明了该问题指数吸引子的存在性.     

一类微分方程零解全局弱吸引和全局吸引到充要条件

考虑二阶微分方程 x =φ(y)-F(x),y=- g(x)q(y) 零解的全局弱吸引和全局吸引性, 说明了Filippov条件(A₂) 不能排除最大椭圆扇形S^* 的存在性, 也不能排除∂S^* 作为其外侧邻域轨线正向极限集的可能. 全面回答了文献[8]末提出的问题;得到了方程(E)满足或不满足Filippov 条件时零解全局弱吸引和全局吸引的一系列充分必要条件, 同时也得到了零解全局渐近稳定的一些新条件.     

一类高阶有理型差分方程的定性研究

主要研究一类高阶有理差分方程的定性问题,证明了方程正解的渐近稳定性、有界性、周期性以及全局吸引性.     

梁方程时间依赖全局吸引子的存在性

研究了梁方程时间依赖吸引子的存在性,在非线性项f满足临界增长条件时,基于时间依赖全局吸引子的存在性定理,应用先验估计和算子分解方法验证了系数参数与时间t有关时,梁方程对应的过程族{U(t,τ)}的渐近紧性,从而得到梁方程时间依赖全局吸引子的存在性及正则性.     

一类广义时滞 Logistic 方程的全局吸引性

本文研究了一类广义时滞Logistic方程的全局吸引性,获得了该方程的正平衡点全局吸引的一个充分条件,对已有的结果进行了改进和推广.     

Stability Properties and Spurious Period Two Solutions in a Numerical Scheme for a Reaction-Diffusion Equation with Nonlinear Diffusion

In previous work a discrete version of a generalized form ofFisher's equation was considered with both linear and a quadraticnonlinear diffusion, and the stability regions of certain periodtwo solutions were calculated. In this paper higher-order nonlinearitiesin the diffusion term are considered. It is shown that termsof order higher than cubic destabilize the period two solutions,in the sense that the stability region becomes smaller thanin the case of linear diffusion. Quadratic diffusion, on theother hand, has the largest stability region. It is also shown that for nonlinear diffusion of sufficientlyhigh order, unstable period two solutions may exist for thesame parameter values as the stable fixed point. Unlike thecase of lower orders of nonlinear diffusion, there is no longera strip of stable period two solutions adjacent to the entireboundary of the stability region of this fixed point. The results of several numerical calculations are given. Theseimply that the basin of attraction of the stable fixed pointbecomes smaller when the order of nonlinearity of the diffusionterm is increased.     

Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrödinger equations with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper are the coupled higher-order nonlinear Schrödinger equations with variable coefficients, which represent the propagation of femtosecond soliton pulses comprising of two fields with the left and right polarization in the inhomogeneous optical fiber media. Infinitely-many conservation laws are obtained based on the Lax pair. Via the Hirota method and symbolic computation, bilinear forms, bilinear Bäcklund transformations, one- and two-soliton-like solutions are also derived. With different coefficients, bell-shaped, periodic-changing, quadratic-varying, exponential-decreasing and exponential-increasing soliton-like profiles are seen, to describe the propagation and interactions of the femtosecond soliton pulses. Head-on and overtaking elastic interactions are shown, which are decided by the directions of the velocities. We also get the bound states with periodic attraction and repulsion between two solitons.     

Higher-Order Solitons in the N-Wave System

The soliton dressing matrices for the higher-order zeros of the Riemann–Hilbert problem for the N -wave system are considered. For the elementary higher-order zero, that is, whose algebraic multiplicity is arbitrary but the geometric multiplicity is 1, the general soliton dressing matrix is derived. The theory is applied to the study of higher-order soliton solutions in the three-wave interaction model. The simplest higher-order soliton solution is presented. In the generic case, this solution describes the breakup of a higher-order pumping wave into two higher-order elementary waves, and the reverse process. In non-generic cases, this solution could describe (i) the merger of a pumping sech wave and an elementary sech wave into two elementary waves (one sech and the other one higher order); (ii) the breakup of a higher-order pumping wave into two elementary sech waves and one pumping sech wave; and the reverse processes. This solution could also reproduce fundamental soliton solutions as a special case.     

Solitary wave solution of higher-order Korteweg–de Vries equation

An attempt has been made to obtain exact analytical traveling wave solution or simple wave solution of higher-order Korteweg–de Vries (KdV) equation by using tanh-method or hyperbolic method. The higher-order equation can be derived for magnetized plasmas by using the reductive perturbation technique. It is found that the exact solitary wave solution of higher-order KdV equation is obtained by tanh-method. Using this method, different kinds of nonlinear wave equations can be evaluated. The higher-order nonlinearity and higher-order dispersive effect can be observed from the solutions of the equations. The method is applicable for other nonlinear wave equations.     

一类不可微规划的高阶对称对偶性

本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .     

Higher-Order Duality in Nondifferentiable Multiobjective Programming

A new generalized class of higher-order (F, α, ρ, d)–type I functions is introduced, and a general Mond–Weir type higher-order dual is formulated for a nondifferentiable multiobjective programming problem. Based on the concepts introduced, various higher-order duality results are established. At the end, some special cases are also discussed.     

Higher-order symmetric duality in multiobjective programming problems under higher-order invexity

In this paper we present a pair of Wolfe and Mond-Weir type higher-order symmetric dual programs for multiobjective symmetric programming problems. Different types of higher-order duality results (weak, strong and converse duality) are established for the above higher-order symmetric dual programs under higher-order invexity and higher-order pseudo-invexity assumptions. Also we discuss many examples and counterexamples to justify our work.     

Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations

In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge–Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge–Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection–diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.     

On higher-order proto-differentiability of perturbation maps

This paper is concerned with higher-order sensitivity analysis in parametric vector optimization problems. Firstly, higher-order proto-differentiability of a set-valued mapping from one Euclidean space to another is defined. Then, we prove that the perturbation map/the proper perturbation map/the weak perturbation map of a parameterized vector optimization problem are higher-order proto-differentiable under some suitable qualification conditions.

     

Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization

Recently Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010) introduced higher-order cone-convex functions and used them to obtain higher-order sufficient optimality conditions and duality results for a vector optimization problem over cones. The concepts of higher-order (strongly) cone-pseudoconvex and cone-quasiconvex functions were also defined by Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010). In this paper we introduce the notions of higher-order naturally cone-pseudoconvex, strictly cone-pseudoconvex and weakly cone-quasiconvex functions and study various interrelations between the above mentioned functions. Higher-order sufficient optimality conditions have been established by using these functions. Generalized Mond–Weir type higher-order dual is formulated and various duality results have been established under the conditions of higher-order strongly cone-pseudoconvexity and higher-order cone quasiconvexity.