Energy Scattering for the Generalized Davey—Stewartson Equations

Abstract Considring the generalized Davey-Stewartson equation i-△u+λ│u│~pu+μE(│u│~q)│u│~(q-2)u=0,where λ>0,μ≥0,E=F~(-1)(ξ_1~2│ξ│~2)F,we obtain the existence of scattering operator in ∑(R~n):u{u∈H~1(R~n):│x│u∈L~2(R~n)}.     

RESEARCH ANNOUNCEMENTS——Dynamical Behavior for the Three-dimensional Generalized Hasegawa-Mima Equations

We consider the following generalized three-dimensional （3-D） dissipative Hasegawa-Mima equations： △ut - ut ＋ {u, △u} ＋ knuy - vz ＋ α△（u - △u） ＋ f（x, y, z） = 0, （1） vt ＋ {u, v} ＋ uz ＋ γv - β△v = g（x, y, z） （2） with initial datum v｜t=0=u0（x,y,z）,v｜t=0=v0（x,y,z）,（x,y,z）∈Ω∈R^3 （3）.     

Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming

In this paper we establish the existence,uniqueness and iterative approximation of solutions fortwo classes of functional equations arising in dynamic programming of multistage decision processes.The resultspresented here extend,and unify the corresponding results due to Bellman,Bhakta and Choudhury,Bhaktaand Mitra,Liu and others.     

Lq Interior Estimates of the Gradient for Weak Solutions of Quasilinear Elliptic Equations

The authors present a new proof of L^q interior estimates of the gradient for weak solutions of a quasilinear elliptic equation of p-Laplacian type.     

On the Existence of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equation

By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.     

Boundedness for a Class of Generalized Commutators on λ-Central Morrey Space

Let 0 ≤α n,Ω be a rough kernel,and let A have derivatives of order m 1 in CBBMOq,μ2 with m ≥ 2.We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type,and obtain the boundedness of TΩA,α from the central Morrey spaces Ep,μ1 to Er,λ for λ = μ1 + μ2 + α/n and 1/r = 1/p + 1/q α/n.     

Asymptotic of the Solutions of the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors（Ⅱ）

The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.     

Local Bifurcation of Critical Periods for a Class of Liénard Equations

In this paper,we study the local bifurcation of critical periods near the nondegenerate center(the origin) of a class of Liénard equations with degree 2n,and prove that at most 2n-2 critical periods(taken into account multiplicity) can be produced from a weak center of finite order.We also prove that it can have exactly2n-2 critical periods near the origin.     

p-adic Transcendence and p-adic Transcendence Measures for the Values of Mahler Type Functions

We prove the p-adic transcendence and p-adic transcendence measures for the values of some Mahler type functions.     

On Monotone Method for Second Order Periodic Boundary Value Problems and Periodic Solutions of Functional Difference Equations

In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution a and upper solution βwith α≤β.     

Lump Solutions,Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations北大核心CSCD

Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the “fusion” and “fission” phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.     

A Half—Power Trace Formulas for the Generalized Jaulent—Miodek Equation

A new dispersive relation is found and a half-pow tormulas for the generalizeMiodek equation under the deeaying conditions at infinity are obtained.     

Generalized Integral Representations for Functions with Values in C（V_（3,3））

By using the solution to the Helmholtz equation u-λu = 0(λ ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.     

Calculus of Generalized Quasi－differentiable Functions Ⅰ：Some Results on the Space of Pairs of Convex－Set Collections

A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions.The space K1 is constructed by introducing a well-defined equivalence reation among pairs of collections of convex sets .Some important properties on the norm and operations is K1 are given.     

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.let Ωn,p1,p2,…,pn={z=(z1,z2,…,zn)'∈Cn:nΣj=1|zj|pj<1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers. In this paper,we will prove that Фn,β2,у2…βn,уn(f)(z)=(f(z1),(f(z1)z1)β2(f'(z1))у2z2,…,(f(z1)z1)βn(f'(z1))уnzn)' Preserves spirallikeness of type β and order α on Ωn,p1,p2,…pn.     

Construction of Green＇s Functions for the Two-Dimensional Static Klein-Gordon Equation

In contrast to the cognate Laplace equation, for which a vast number of Green＇s functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green＇s functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computerfriendly representations of their Green＇s functions are obtained, most of which have never been published before.