共查询到20条相似文献，搜索用时 84 毫秒
1.
In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations |
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2.
We study properties of solutions f, g, h C(G) of the functional equation |
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3.
A second order nonlinear differential equation |
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4.
Let h(t) be an arbitrary bounded radial function and let ( x) be a real measurable and radial function defined on R
n–1. For x, yR
n–1, we establish that the singular integral along surface x ( x, ( x)): and the associated maximal singular integral are bounded in L
p( R
n) for 1< p<, n3, provided that the maximal operator is bounded on L
p
(R) for all 1< p. 相似文献
5.
Let X be a locally compact abelian group and let a compact group G act on X. We find solutions f: X in L(X) of the following functional equation: |
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6.
We solve the functional equation |
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7.
We consider first the initial-boundary value problem for the parabolic equation |
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8.
Let
We show that for every function
satisfying the conditional equation
|
0,{\text{ then }}f(x + f(x)y) = f(x)f(y)
$$
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|
either there exists a solution
of the Goab-Schinzel equation
such that
(i.e., f( x) = g( x) for
) or there is x0 > 0 with f( x0) < –1 and f( x) = 0 for x x0 . In particular we determine the solutions
of the conditional equation that are continuous at a point, Lebesgue measurable or Baire measurable (i.e., have the Baire property). In this way we solve some problems raised by the first author.Received: 2 March 2004 相似文献
9.
A bi-Lipschitz continuous mapping of a space X is a bijection
such that
, where
. We write
if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by
the set of all bi-Lipschitz mappings of X that are not isometry. Thus,
if
and blip
. For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows:
where
Bibliography: 2 titles. 相似文献
10.
Necessary and sufficient conditions have been found to force all solutions of the equation to behave in peculiar ways. These results are then extended to the elliptic equation where is the Laplace operator and p 3 is an integer. 相似文献
11.
We prove the maximum principle for an optimal control problem governed by the system with state constraint
, under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2)
a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case
, with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems. 相似文献
12.
In this paper, we discuss the conditions for a center for the generalized Liénard system (E) 1
or (E) 1
with f(x), g(x),(y),\ (y),\ h(y)\colon , F(x) = 0 x f(x)dx, and xg( x) > 0 for x 0. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2]. 相似文献
13.
Equivalence theorems concerning the convergence of the Bernstein polynomials B
n
f are well known for continuous functions f in the sup-norm. The purpose of this paper is to extend these results for functions f, Riemann integrable on [0, 1], We have therefore to consider the seminorm |
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14.
Let
be a semilinear hyperbolic system, where A is a real diagonal matrix and a mapping yF(x, t, y) is in
with uniform bounds for ( x, t) K 2. Oberguggenberger [6] has constructed a generalized solution to (1) when A is an arbitrary generalized function and F has a bounded gradient with respect to y for ( x, t) K 2. The above system, in the case when the gradient of the nonlinear term F with respect to y is not bounded, is the subject of this paper. F is substituted by F
h() which has a bounded gradient with respect to y for every fixed (, ) and converges pointwise to F as 0. A generalized solution to is obtained. It is compared to a continuous solution to (1) (if it exists) and the coherence between them is proved. 相似文献
15.
The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach space X
On the real line and of
On the half-line are studied. Assuming that the inhomogeneity f (resp. g) belongs to a given homogeneous subspace of BUC(X) (resp. BUC(
+;X)) it is shown that given bounded solutions u (resp. v) belong also to provided the spectra of these equations are countable. The results are applied to an equation of scalar type which is of importance in applications like viscoelasticity. 相似文献
16.
We investigate spectral properties of operators on H2 of the form
We describe the fine spectrum when g is a rational function. We also provide useful relations for these operators in the Calkin algebra.Submitted: August 21, 2003 相似文献
17.
In this paper we solve the equations |
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18.
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
19.
Summary. Let be given continuous functions on the interval I such that g ≠ 0, and is strictly monotonic (thus invertible) on I. Taking an increasing nonconstant function μ on [0, 1] is a mean value of . Here we solve the homogeneity equation
for two important special cases of symmetric means of this type: for the quasi-arithmetic means weighted by a weight function
and for the Cauchy means. We assume that is open, , and f, g satisfy strong differentiability conditions.
Research supported by OTKA grants T 043080, T 047373. 相似文献
20.
In this paper, we consider the following second-order three-point boundary value problem
where f : [0, 1] × R2 R is continuous, > 0, 0 < < 1 such that < 1. We give conditions on f and two pairs of lower and upper solutions to ensure the existence of at least three solutions of the given problem. Our method is based upon Leray-Schauder degree theory. The emphasis here is that f depends on the first derivative. Our results extend some results in the references.Received: 17 June 2004 相似文献
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