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1.
    
《Analysis Mathematica》1976,2(3):203-210
B p, (r) (R n ) l l p . B p, (r) (R n ) «» .  相似文献   

2.
. , A 0,A 1,— - lim supA j - H, . , - - . , , ; , , . - . - .  相似文献   

3.
Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in 2n+1. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions.  相似文献   

4.
Lower bounds are obtained for solutions of the initial-boundary Dirichlet problem for high order equations. Sharp bounds are also obtained for ess sup¦u(x, t)¦ of the Neumann initial-boundary problem for a second- order equation in D=x(t >0), where (Rn, n 2 is a domain with noncompact convex boundary.Translated from Ukrainskii Maternaticheskii Zhurnal, Vol. 44, No. 10, pp. 1441–1450, October, 1992.  相似文献   

5.
In this paper we study particular sets of a Steiner systemS. More precisely, we study the setsA such that ¦A ¦ d modh for all lines ofS, withd andh integers satisfyingd 0,h 2.Dedicated to Professor M. Scafati Tallini on the occasion of her sixtyfifth birthday  相似文献   

6.
In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup of convex characteristic functions on the semiaxis (0,). Letn ()={:1¦11 or 1=}, and Io()={: 1¦ 1 N()}. The following results are proved: 1) The semigroup is almost delphic in the sense of R. Davidson. 2) N() is a set of the type G which is dense in (in the topology of uniform convergence on compacta). 3) The class Io() contains only the function identically equal to one.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 717–725, May, 1977.The author thanks I. V. Ostrovskii for the formulation of the problem and valuable remarks.  相似文献   

7.
Analogues of the well known in the theory of analytic functions Phragmén-Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div(|u|–2u)=f(x, u), where the function f(x, u) is locally bounded in IRn+1,f(x, 0)=0,uf(x, u)a¦u¦1+q,a>0,>1,-1>q0, n>/2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 279–283, February, 1992.  相似文献   

8.
Summary We prove the existence of nontrivial solutions for nonlinear equations of the type Lu=g(x, u) + ¦u¦¯p–2u, ¯ p > 2, where L is a continuous self- adjoint linear operator in a Hilbert space H and ug(x, u) is a lower order perturbation of ¦u¦¯p–1. We assume that ¯p is the critical exponent in the sense that the embedding H Lp, If is compact for 1p<¯p and is continuous (not necessarily compact) for p=¯p. From this result we deduce, for example, that utt -u- u=¦u¦2/Nu, u L2(SN×S1) has at least one pair (–u, u) of solutions nonconstant with respect to t, provided that is sufficiently close to some eigenvalue of tt–.Work supported by M.P.I. Italy (fondi 40%, 60%) and by G.N.A.F.A. of C.N.R.  相似文献   

9.
Range of the posterior probability of an interval over the -contamination class ={=(1–)0+q:qQ} is derived. Here, 0 is the elicited prior which is assumed unimodal, is the amount of uncertainty in 0, andQ is the set of all probability densitiesq for which =(1–)0+q is unimodal with the same mode as that of 0. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1–)0 except in one interval (resp. two disjoint intervals) where it is constant.  相似文献   

10.
Continuing the research of part I conditions equivalent to ()- or ()-nuclearity of spaces of ultradifferential functions and their duals as well as some applications are given. To get these results it is shown that tensor products of smooth sequence spaces, power series spaces, and spaces S(Mq) introduced in part I are isomorphic to suitable sequence spaces of the same class, which are stable provided the factors are stable power series spaces. Hence it is possible to establish isomorphisms between different functions spaces, to calculate the nuclearity types of tensor products by the nuclearity types of the factors, and to prove that the class of ()- or ()-nuclear spaces is closed under forming tensor products iff is multiplicatively stable.  相似文献   

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