共查询到20条相似文献,搜索用时 718 毫秒
1.
Nonlinear partial differential operators having the form G(u) = g(u, D1u,…, DNu), with g?C(R × RN), are here shown to be precisely those operators which are local, (locally) uniformly continuous on, , and (roughly speaking) translation invariant. It is also shown that all such partial differential operators are necessarily bounded and continuous with respect to the norm topologies of . 相似文献
2.
In a recent paper [3] the authors derived maximum principles which involved , where u(x) is a classical solution of an alliptic differential equation of the form (. In this paper these results are extended to the more general case in which is replaced by h(u, q2). 相似文献
3.
Robert Donaghey 《Journal of Combinatorial Theory, Series A》1979,27(3):360-364
It is shown that the compositional inverse of either of two transformations of a given series can be determined from the compositional inverse of the series. Specifically, if t · f(t) and t · g(t) are compositional inverses, then so are t · fk(t) and , where fk(t) is the kth Euler transformation of f(t) and . 相似文献
4.
Georg Lindgren 《Journal of multivariate analysis》1980,10(2):181-206
Let ζ(t), η(t) be continuously differentiable Gaussian processes with mean zero, unit variance, and common covariance function r(t), and such that ζ(t) and η(t) are independent for all t, and consider the movements of a particle with time-varying coordinates (ζ(t), η(t)). The time and location of the exists of the particle across a circle with radius u defines a point process in R3 with its points located on the cylinder {(t, u cos θ, u sin θ); t ≥ 0, 0 ≤ θ < 2π}. It is shown that if r(t) log t → 0 as t → ∞, the time and space-normalized point process of exits converges in distribution to a Poisson process on the unit cylinder. As a consequence one obtains the asymptotic distribution of the maximum of a χ2-process, χ2(t) = ζ2(t) + η2(t), P{sup0≤t≤Tχ2(t) ≤ u2} → e?τ if as T, u → ∞. Furthermore, it is shown that the points in R3 generated by the local ?-maxima of χ2(t) converges to a Poisson process in R3 with intensity measure (in cylindrical polar coordinates) (2πr2)?1dtdθdr. As a consequence one obtains the asymptotic extremal distribution for any function g(ζ(t), η(t)) which is “almost quadratic” in the sense that has a limit as r → ∞. Then if as T, u → ∞. 相似文献
5.
《Journal de Mathématiques Pures et Appliquées》2002,81(9):827-846
We consider the system Δu=p(x)g(v), Δv=q(x)f(u) in , where f,g are positive and non-decreasing functions on (0,∞) satisfying the Keller–Osserman condition and we establish the existence of positive solutions that blow-up at infinity. 相似文献
6.
A mean M(u, v) is defined to be a homogeneous symmetric function of two positive real variables satisfying min(u, v) ? M(u, v) ? max(u, v) for all u and v. Setting M(u, v) = uM(1, vu?1) = uM(1, 1 ? t), 0 ? t < 1, we determine power series expansions in t of various generalized means, including (Stolarsky's mean), (Lehmer's mean), (Leach and Sholander's mean), and (Gini's mean). The explicit power series coefficients and recurrence relations for these coefficients are found. Finally, applications are shown by proving a theorem that generalizes one due to Lehmer. 相似文献
7.
Consider the renewal equation in the form (1) , where is a probability density on [0, ∞) and limt → ∞g(t) = g0. Asymptotic solutions of (1) are given in the case when f(t) has no expectation, i.e., . These results complement the classical theorem of Feller under the assumption that f(t) possesses finite expectation. 相似文献
8.
According to a result of A. Ghizzetti, for any solution y(t) of the differential equation where , (0 ?i ? n ?1, either y(t) = 0 for t ? 1 or there is an integer r with 0 ? r ? n ? 1 such that exists and ≠0. Related results are obtained for difference and differential inequalities. A special case of the former has interesting applications in the study of orthogonal polynomials. 相似文献
9.
S. Ihara 《Journal of multivariate analysis》1974,4(1):74-87
The message m = {m(t)} is a Gaussian process that is to be transmitted through the white Gaussian channel with feedback: . Under the average power constraint, , we construct causally the optimal coding, in the sense that the mutual information It(m, Y) between the message m and the channel output Y (up to t) is maximized. The optimal coding is presented by , where and A(s) is a positive function such that . 相似文献
10.
Hans G Kaper 《Journal of Mathematical Analysis and Applications》1978,63(3):691-718
In this article we discuss the solution of boundary value problems which are described by the linear integrodifferential equation , where t∈J?, x∈. We interpret the equation in functional form as an ordinary differential equation for the mapping u:J→L2(R,μ), where L2(R,μ) is a weighted L2-space. Emphasis is on the constructive aspects of the solution and on finding representations of the relevant isomorphisms. 相似文献
11.
William Layton 《Journal of Mathematical Analysis and Applications》1980,77(1):198-204
Existence and uniqueness of 2π-periodic solutions of , where x(t) is in n and e(t, u, v) is a given vector function, 2π-periodic in t, are shown under conditions on the spectrum of the Hessian of G. The equation is studied using a fixed point theorem in the space L2(0, 2π). One feature of this approach is that no relationship between the delay and the period is necessary. 相似文献
12.
《Nonlinear Analysis: Theory, Methods & Applications》2004,56(2):185-199
In this paper we are concerned with positive solutions of the doubly nonlinear parabolic equation ut=div(um−1|∇u|p−2∇u)+Vum+p−2 in a cylinder , with initial condition u(·,0)=u0(·)⩾0 and vanishing on the parabolic boundary . Here (resp. ) is a bounded domain with smooth boundary, , , 1<p<N and m+p−2>0. The critical exponents are found and the nonexistence results are proved for . 相似文献
13.
This paper deals with asymptotic behavior for (weak) solutions of the equation , on + × Ω; u(t, x) = 0, on + × ?Ω. If and β is coercive, we prove that the solutions are bounded in the energy space, under weaker assumptions than those used by G. Prouse in a previous work. If in addition and ? is srongly almost-periodic, we prove for strongly monotone β that all solutions are asymptotically almost-periodic in the energy space. The assumptions made on β are much less restrictive than those made by G. Prouse: mainly, we allow β to be multivalued, and in the one-dimensional case β need not be defined everywhere. 相似文献
14.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
15.
In this paper we study the existence, uniqueness, and regularity of the solutions for the Cauchy problem for the evolution equation is in (0, 1), 0 ? t ? T, T is an arbitrary positive real number,f(s)?C1, and g(x, t)?L∞(0, T; L2(0, 1)). We prove the existence and uniqueness of the weak solutions for (1) using the Galerkin method and a compactness argument such as that of J. L. Lions. We obtain regular solutions using eigenfunctions of the one-dimensional Laplace operator as a basis in the Galerkin method. 相似文献
16.
Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
17.
We investigate the boundary value problem , , u(?∞, t) = v(∞, t) = 0, u(∞, t) = 1, and v(?∞, t) = γ ?t > 0 where r > 0, b > 0, γ > 0 and x?R. This system has been proposed by Murray as a model for the propagation of wave fronts of chemical activity in the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We determine the global stability of the constant solution (u, v) ≡ (1,0). Furthermore we introduce a moving coordinate and for each fixed x?R we investigate the asymptotic behavior of u(x + ct, t) and v(x + ct, t) as t → ∞ for both large and small values of the wave speed c ? 0. 相似文献
18.
The existence of a unique strong solution of the nonlinear abstract functional differential equation , (E) is established. X is a Banach space with uniformly convex dual space and, for is m-accretive and satisfies a time dependence condition suitable for applications to partial differential equations. The function F satisfies a Lipschitz condition. The novelty of the paper is that the solution u(t) of (E) is shown to be the uniform limit (as n → ∞) of the sequence un(t), where the functions un(t) are continuously differentiate solutions of approximating equations involving the Yosida approximants. Thus, a straightforward approximation scheme is now available for such equations, in parallel with the approach involving the use of nonlinear evolution operator theory. 相似文献
19.
Ming-Po Chen Cheh-Chih Yeh Cheng-Shu Yu 《Journal of Mathematical Analysis and Applications》1977,59(2):211-215
For nonlinear retarded differential equations and the sufficient conditions are given on fi, pi, Fi, and h under which every bounded nonoscillatory solution of () or () tends to zero as t → ∞. 相似文献
20.
R Lowen 《Journal of Mathematical Analysis and Applications》1978,64(2):446-454
Starting from a defining differential equation of the kernel of an exponential operator with normalization ∫?∞∞W(λ, t, u) du = 1, we determine Sλ for various p(t) including; for example, p(t) a quadratic polynomial, all the known exponential operators are recovered and some new ones are constructed. It is shown that all the exponential operators are approximation operators. Further approximation properties of these operators are discussed. For example, functions satisfying are characterized. Several results of C. P. May are also improved. 相似文献