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1.
Let , let and let be a bounded domain with a smooth boundary . Our purpose in this paper is to consider the existence of solutions of the problem: where 相似文献
2.
Let 1$">, and be a rational function with numerator, denominator of degree , respectively. In several applications, one needs to know the size of the set such that for , In an earlier paper, we showed that where denotes linear Lebesgue measure. Here we obtain, for each , the sharp version of this inequality in terms of condenser capacity. In particular, we show that as , 相似文献
3.
Given a family of vectors in a Hilbert space we characterize the existence of a family of commuting contractions on having regular dilation and such that The theorem is a multi-dimensional analogue for some well-known operator moment problems due to Sebestyén in case or, recently, to Gavruta and Paunescu in case . 相似文献
4.
The main theorem of this note is the following refinement of the well-known Lelong-Bremermann Lemma: Let be a continuous plurisubharmonic function on a Stein manifold of dimension Then there exists an integer , natural numbers , and analytic mappings such that the sequence of functions converges to uniformly on each compact subset of . In the case when is a domain in the complex plane, it is shown that one can take in the theorem above (Section 3); on the other hand, for -circular plurisubharmonic functions in the statement of this theorem is true with (Section 4). The last section contains some remarks and open questions. 相似文献
5.
We consider the derivative nonlinear Schrödinger equations where the coefficient satisfies the time growth condition is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when 相似文献
6.
Let be a sequence of distinct positive numbers. Let and let denote the extremal Müntz polynomial in with exponents . We investigate the zero distribution of . In particular, we show that if then the normalized zero counting measure of converges weakly as to while if or , the limiting measure is a Dirac delta at or , respectively. 相似文献
7.
Here is a particular case of the main result of this paper: Let be a bounded domain, with a boundary of class , and let be two continuous functions, , with 0$">, , with n$">. If and if the set of all global minima of the function has at least connected components, then, for each 0$"> small enough, the Neumann problem admits at least strong solutions in . 相似文献
8.
In this paper we give asymptotic estimates of the least energy solution of the functional as goes to infinity. Here is a smooth bounded domain of . Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that . 相似文献
9.
In 1992, P. Polácik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on with Neumann boundary condition provided that there exists a smooth vector field on such that In this short paper, we give a classification of all the domains on which one may find such a type of vector field. 相似文献
10.
For , a bounded domain, and for , we improve the Hardy-Sobolev inequality by adding a term with a singular weight of the type . We show that this weight function is optimal in the sense that the inequality fails for any other weight function more singular than this one. Moreover, we show that a series of finite terms can be added to improve the Hardy-Sobolev inequality, which answers a question of Brezis-Vazquez. Finally, we use this result to analyze the behaviour of the first eigenvalue of the operator as increases to for . 相似文献
11.
It is well known that the Green function of the standard discrete Laplacian on , exhibits a pathological behavior in dimension . In particular, the estimate fails for . This fact complicates the study of the scattering theory of discrete Schrödinger operators. Molchanov and Vainberg suggested the following alternative to the standard discrete Laplacian, and conjectured that the estimate holds for all . In this paper we prove this conjecture. 相似文献
12.
Let be i.i.d. random variables with , and set . We prove that, for under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974). 相似文献
13.
For a function defined on an interval let The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let be an integer. Let be distinct real numbers. Let . Then where the supremum is taken for all (the span is the linear span over ). 相似文献
14.
We show that if is a finite group, a conjugacy class of and , are the distinct elements in the multiset (here is the value of on any element of ), then This is a dual to a generalization of a theorem of Blichfeldt stating that if is a finite group, a generalized character and are the distinct values of , then We also observe that in Blichfeldt's congruence can be replaced, with a minor adjustment, by any rational value of . A similar change can be done to the first congruence above. 相似文献
15.
We consider a circular, bounded, strictly convex domain with boundary of class . For any compact subset of we construct a sequence of homogeneous polynomials on which are big at each point of . As an application for any circular subset of type we construct a holomorphic function which is square integrable on and such that where denotes unit disc in . 相似文献
16.
Let be a bounded domain such that . Let be a (P.S.) sequence of the functional . We study the limit behaviour of and obtain a global compactness result. 相似文献
17.
In this note we introduce a dyadic one-sided maximal function defined as where is a certain cube associated with the dyadic cube and . We characterize the pair of weights for which the maximal operator applies into weak- for . 相似文献
18.
Let denote a sequence of measurable functions on , and let denote the weak norm. It is shown that where is a sequence of independent random variables taking on values and with equal probability. Moreover, it is shown that The paper concludes by providing an example indicating that, if , then the estimate is the best possible. 相似文献
19.
We consider the nonlinear eigenvalue problem in , on , where is a bounded open set in with smooth boundary and , are continuous functions on such that , , and for all . The main result of this paper establishes that any sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle. 相似文献
20.
The generalized Bochner-Riesz operator may be defined as where is an appropriate distance function and is the inverse Fourier transform. The behavior of on is described for , a rough distance function. We conjecture that this operator is bounded on when and , and unbounded when . This conjecture is verified for large ranges of . 相似文献
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