负载网络参数对E类放大器输出电压的影响

在任意Q值和任意占空比D情况下对E类开关模调谐功率放大器进行了分析,根据谐振回路中电容值的大小,导出了放大器的工作方程,并用拉普拉斯方法,对放大器电路方程进行了求解。结果显示,当放大器的负载网络取不同参数值时,分别得到高Q值的正弦输出电压和低Q值的非正弦输出电压。在最佳工作条件下,给出了集电极电流和集电极——发射极电压波形。

分形双孔介质封闭油气藏的试井模型

针对分形双孔介质模型,对于裂缝介质和岩块介质分别引入了反映分形体的几何特征的分形维数及分形渗流网络连通状况的分形指数;建立了外边界封闭且考虑井筒储存和表皮效应下的变流率问题的试井分析数学模型;并对一类具有广泛应用的特例,求得了无因次地层压力和井底压力的拉普拉斯空间解,归纳出了几个通用公式,并作了进一步应用的讨论,极大地方便和引导了相应的应用,对油气藏数值模拟具有指导意义。

Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.

Positive Solutions of p-Laplacian Functional Difference Equations

In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.

Five Nontrivial Solutions of p-Laplacian Problems Involving Critical Exponents and Singular Cylindrical Potential

In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem

关于矢量的定义以及矢量分析在平面矢场一的些应用(下)

本文从数学史角度研究矢量的定义,以及矢量分析在平面夫场上的一些应用。其次,对于应用狄利克雷原理在求解拉普拉斯方程给出一些有关历史评注。

关于矢量的定义以及矢量分析在平面矢场上的一些应用(上)

本文从数学史角度研究矢量的定义,以及矢量分析在平面矢场上的一些应用。其次,对于应用狄利克雷原理在求解拉普拉斯方程给出一些有关历史评注。

接地导电圆环对称轴上点电荷的电场分布

本文利用环面坐标系的拉普拉斯方程,严格地求解接地导电圆环对称轴上点电荷的电场分布,采用了特殊的办法处理边界条件,还讨论了环面上的电荷面密度分布。

Solutions of Laplace Equation in n-Dimensional Spaces

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.

Existence of solutions for a critical fractional Kirchhoff type problem in(49)R^N

This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity：where （-△）s is the fractional Laplacian operator with 0 〈 s 〈 1, 2s＊ = 2N/（N - 2s）, N 〉 2s, p ∈ （1,2s＊）, θ∈ [1, 2s＊/2）, h is a nonnegative function and A is a real positive parameter. Using the Ekeland variational principle and the mountain pass theorem, we obtain the existence and multiplicity of solutions for the above problem for suitable parameter A 〉 0. Furthermore, under some appropriate assumptions, our result can be extended to the setting of a class of nonlocal integro-differential equations. The remarkable feature of this paper is the fact that the coefficient of fractional Laplace operator could be zero at zero, which implies that the above Kirchhoff problem is degenerate. Hence our results are new even in the Laplacian case.

SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATION IN R^n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at least two solutions if 0 〈 λ 〈 A; at least one solution if λ= A; and no solutions if λ〉A.

EXISTENCE,MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS

This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.

On Singular Sets of Local Solutions to p-Laplace Equations

The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the

The existence and concentration of weak solutions to a class of p-Laplacian type problems in unbounded domains

In this paper,we study the existence and concentration of weak solutions to the p-Laplacian type elliptic problem-εp△pu+V(z)|u|p-2u-f(u)=0 in Ω,u=0 on ■Ω,u>0 in Ω,N>p>2,where Ω is a domain in RN,possibly unbounded,with empty or smooth boundary,εis a small positive parameter,f∈C1(R+,R)is of subcritical and V:RN→R is a locally Hlder continuous function which is bounded from below,away from zero,such that infΛV<min ■ΛV for some open bounded subset Λ of Ω.We prove that there is anε0>0 such that for anyε∈(0,ε0],the above mentioned problem possesses a weak solution uεwith exponential decay.Moreover,uεconcentrates around a minimum point of the potential V inΛ.Our result generalizes a similar result by del Pino and Felmer(1996)for semilinear elliptic equations to the p-Laplacian type problem.

Least energy solutions of nonlinear Schr odinger equations involving the fractional Laplacian and potential wells

We are concerned with the existence of least energy solutions of nonlinear Schrodinger equations involving the fractional Laplacian（-△）%s u（x）＋λV（x）u（x）=u（x）^（p-1）,u（x）〉=0,x∈R^N,for sufficiently large λ,2〈p〈N-2s^-2N for N≥2. V（x） is a real continuous function on RN. Using variational methods we prove the existence of least energy solution uλ（x） which localizes near the potential well int V-1 （0） for A large. Moreover, if the zero sets int V-1 （0） of V（x） include more than one isolated component, then ux（x） will be trapped around all the isolated components. However, in Laplacian case s = 1, when the parameter A is large, the corresponding least energy solution will be trapped around only one isolated component and become arbitrarily small in other components of int V^-1（0）. This is the essential difference with the Laplacian problems since the operator （-△）s is nonlocal.

SCALAR CURVATURES ON NONCOMPACT RIEMANN MANIFOLDS

The author obtains some theorems for a function to be the scalar curvature of some complete conformal metric of a noncompact complete Riemann manifold, and also presents a kind of manifolds oil which Yamabe problem is unsolvable.

Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition

The authors study the p(x)-Laplacian equations with nonlinear boundary condi- tion. By using the variational method, under appropriate assumptions on the perturbation terms f1(x,u), f2(x,u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.