共查询到20条相似文献，搜索用时 31 毫秒
1.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0,
is the Laplacian in
. 相似文献
2.
In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form
where n 3 is odd, > 0, > 0.This research was supported by the grants 1/8055/01 and 1/0026/03 of Scientific Grant Agency of Ministry of Education of Slovak Republic and Slovak Academy of Sciences. 相似文献
3.
Ram U. Verma 《Journal of Computational Analysis and Applications》2002,4(3):177-192
Consider the convergence of the projection methods based on an extension of a special class of algorithms for the approximation--solvability of the following class of nonlinear quasivariational inequality (NQVI) problems: find an element
such that
and
where
are mappings on H and K is a nonempty closed convex subset of a real Hilbert space H. The iterative procedure is characterized as a nonlinear quasivariational inequality: for any arbitrarily chosen initial point x
0 K and, for constants
0$$
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and
0$$
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, we have
where
This nonlinear quasivariational inequality type algorithm has an equivalent projection formula
where
for the projection P
K
of H onto K. 相似文献
4.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
5.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
moreover, for
it is impossible to decrease the constants on
. Here,
are some explicitly constructed constants,
is the modulus of continuity of order r for the function f, and
are explicitly constructed linear operators with the values in the space of periodic splines of degree
of minimal defect with 2n equidistant interpolation points. This assertion implies the sharp Jackson-type inequality
. Bibliography: 17 titles. 相似文献
6.
In this paper we establish the existence of nontrivial solutions to
with V
x superlinear in x. 相似文献
7.
Bhagat Singh 《Czechoslovak Mathematical Journal》2000,50(3):627-639
Qualitative comparison of the nonoscillatory behavior of the equations
and
is sought by way of finding different nonoscillation criteria for the above equations, L
n is a disconjugate operator of the form
Both canonical and noncanonical forms of L
n have been studied. 相似文献
8.
Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
and
for all
Moreover, if
is the least possible value of the exponent in this inequality, then
Deceased.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 579–594, May, 2004. 相似文献
9.
Jan Čermák 《Czechoslovak Mathematical Journal》2000,50(4):825-837
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation
of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution y(x) which behaves in this way. 相似文献
10.
Let be the set of nonnegative integers and the ring of integers. Let
be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of
yields that the subrings generated by them coincide. This subring is the sum of the ideal
consisting of all matrices in
with only a finite number of nonzero entries and the subring of
generated by the identity matrix. Regular elements are also described. We characterize all ideals of
, show that all ideals are finitely generated and that not all ideals of
are principal. Some general ring theoretic properties of
are also established. 相似文献
11.
In this paper we consider the weakly coupled elliptic system with critical growth
where a, b, c, d are C
1-functions defined in a bounded regular domain of
N
. Here we construct families of solutions which blow-up and concentrate at some points in as the positive parameter goes to zero.*The authors are supported by M.I.U.R., project Metodi variazionali e topologici nello studio di fenomeni non lineari. 相似文献
12.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
where c is a real number with
with (t) < t and
.Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which c is a function of t and a certain type of a forcing term is present. 相似文献
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13.
A. K. Prykarpatsky D. L. Blackmore Ya. V. Mykytyuk 《Journal of Mathematical Sciences》2001,104(5):1411-1421
This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])
for a solution to the Hamilton–Jacobi nonlinear partial differential equation
where the Cauchy data
are now a function semicontinuous from below,
is the usual norm in
,
, and
is a positive evolution parameter. We proved that the Lax formula solves the Cauchy problem (2) at all points
,
fixed save for an exceptional set of points R of the F
type, having zero Lebesgue measure. In addition, we formulate a similar Lax-type formula without proof for a solution to a new nonlinear equation of the Hamilton–Jacobi-type:
where
is a diagonal positive-definite matrix, mentioned in Part I and having interesting applications in modern mathematical physics. 相似文献
14.
Satoshi Tanaka 《Czechoslovak Mathematical Journal》2001,51(3):573-583
The higher order neutral functional differential equation
is considered under the following conditions:
is strictly increasing in
is nonnegative on
and nondecreasing in
. A necessary and sufficient condition is derived for the existence of certain positive solutions of (1). 相似文献
15.
C. S. Lin 《Czechoslovak Mathematical Journal》2002,52(3):665-672
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for
must be unbounded, provided
, in
and for every bounded subset I, f(t, z) is bounded in E × I.(B) Every bounded solution for
, in
, must be constant, provided
in
and for every bounded subset I,
is bounded in
. 相似文献
16.
In this paper we prove an existence theorem for the Cauchy problem
using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness. 相似文献
17.
The Maurey–Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some Lp()(0) which satisfies a vector-valued norm inequality
even allows a weighted norm inequality: there is a function 0wL
0() such that
Continuing the work of Garcia-Cuerva and Rubio de Francia we give several scalar and vector-valued variants of this fundamental result within the framework of quasi Köthe function spaces X() over measure spaces. They are all special cases of our main result (Theorem 2) which extends the Maurey–Rosenthal cycle of ideas to the case of homogeneous operators between vector spaces being homogeneously representable in quasi Köthe function spaces. 相似文献
18.
G. A. Kalyabin 《Functional Analysis and Its Applications》2004,38(3):184-191
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
Specifically, we prove that
for all and k{0,...,n-1}. We establish symmetry and regularity properties of the numbers A
n,k
and study their asymptotic behavior as n for the cases k=O(n
2/3) and k/n(0,1).Similar problems were previously studied by Gabushin and Taikov. 相似文献
19.
W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let E/E be a 1-parameter closed planar Euclidean motion with the rotation number and the period T. Under the motion E/E, let two points A = (0, 0), B = (a + b, 0) E trace the curves k
A, k
B E and let F
A, F
B be their orbit areas, respectively. If F
X is the orbit area of the orbit curve k of the point X = (a, 0) which is collinear with points A and B then
In this paper, under the 1-parameter closed planar homothetic motion with the homothetic scale h = h(t), the generalization given above by W. Blaschke and H. R. Müller is expressed and
is obtained, where
相似文献
20.
Let
be sequences of real numbers which are symmetric in k. Let
be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of
we consider
Let
Several examples are given in which the condition
is either a sufficient, a necessary, or a necessary and sufficient condition for {Q(x), x[0, 2]
n
} to have a continuous version. 相似文献