共查询到20条相似文献,搜索用时 31 毫秒
1.
Tomasz Człapiński 《Czechoslovak Mathematical Journal》1999,49(4):791-809
We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order
where
is a function defined by z
(x,y)(t, s) = z(x + t, y + s), (t, s) [–, 0] × [0, h]. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem. 相似文献
2.
L. S. Zaremba 《Journal of Optimization Theory and Applications》1979,29(1):135-145
This paper is strictly related to Ref. 1. A pursuit-evasion game described in part by the system
and
is considered. The state variablesx andy are restricted, in the sense that (x(t),t) N
1 and (y(t),t) N
2. The existence of a value in the sense of Varaiya and Lin is proved under the assumption that the sets of all admissible trajectories for the two players are compact and the lower value is not greater than the upper value. 相似文献
3.
Donal O'Regan 《Czechoslovak Mathematical Journal》1998,48(2):269-289
Existence results are established for the resonant problem y + m
a y = f(t, y) a.e. on [0, 1] with y satisfying Dirichlet boundary conditions. The problem is singular since f is a Carathéodory function,
with a > 0 a.e. on [0, 1] and
相似文献
4.
WEN GuoChun LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2008,51(1):5-36
The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line K_1(y)u_(xx) |K_2(x)|u_(yy) a(x,y)u_x b(x, y)u_y c(x,y)u=-d(x,y) in any plane domain D with the boundary D=Γ∪L_1∪L_2∪L_3∪L_4, whereΓ(■{y>0})∈C_μ~2 (0<μ<1) is a curve with the end points z=-1,1. L_1, L_2, L_3, L_4 are four characteristics with the slopes -H_2(x)/H_1(y), H_2(x)/H_1(y),-H_2(x)/H_1(y), H_2(x)/H_1(y)(H_1(y)=|k_1(y)|~(1/2), H_2(x)=|K_2(x)|~(1/2) in {y<0}) passing through the points z=x iy=-1,0,0,1 respectively. And the boundary condition possesses the form 1/2 u/v=1/H(x,y)Re[λuz]=r(z), z∈Γ∪L_1∪L_4, Im[λ(z)uz]|_(z=z_l)=b_l, l=1,2, u(-1)=b_0, u(1)=b_3, in which z_1, z_2 are the intersection points of L_1, L_2, L_3, L_4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations K_1(y)(M_2(x)u_x)_x M_1(x)(K_2(y)u_y)_y r(x,y)u=f(x,y), in D as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u_(xx) u_(yy)=0 with the boundary condition u(z)=φ(z) onΓ∪L_1∪L_4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin- Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z)=W(x iy)=u_z=[H_1(y)u_x-iH_2(x)u_y]/2 in the elliptic domain and W(z)=W(x jy)=u_z=[H_1(y)u_x-jH_2(x)u_y]/2 in the hyperbolic domain are introduced for the first time, such that the second order equations of mixed type can be reduced to the mixed complex equations of first order with singular coefficients. And thirdly, the advantage of complex analytic method is used, otherwise the complex analytic method cannot be applied. 相似文献
5.
A. M. Shelekhov 《Aequationes Mathematicae》1991,41(1):79-84
A loopQ(·) is said to be anA
l-loop (A
r-loop) if x, y Q, l
x,y AutQ (r
x,y AutQ) hold, where
相似文献
6.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(1):79-97
It is shown that every almost linear mapping
of a unital Poisson JC*-algebra
to a unital Poisson JC*-algebra
is a Poisson JC*-algebra homomorphism when h(2
n
uy) = h(2
n
u) h(y), h(3
n
u y) = h(3
n
u) h(y) or h(q
n
u y) = h(q
n
u) h(y) for all
, all unitary elements
and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative mapping
is a Poisson JC*-algebra homomorphism when h(2x) = 2h(x), h(3x) = 3h(x) or h(qx) = qh(x) for all
. Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings.Moreover, we prove the Cauchy–Rassias stability of Poisson JC*-algebra homomorphisms in Poisson JC*-algebras.*This work was supported by grant No. R05-2003-000-10006-0 from the Basic Research Program of the Korea Science & Engineering Foundation. 相似文献
7.
This paper considers the solution of the problem: inff[y, x(y)] s.t.y
[y, x(y)] E
k
, wherex(y) solves: minF(x, y) s.t.x R(x, y) E
n
. In order to obtain local solutions, a first-order algorithm, which uses {dx(y)/dy} for solving a special case of the implicitly definedy-problem, is given. The derivative is obtained from {dx(y, r)/dy}, wherer is a penalty function parameter and {x(y, r)} are approximations to the solution of thex-problem given by a sequential minimization algorithm. Conditions are stated under whichx(y, r) and {dx(y, r)/dy} exist. The computation of {dx(y, r)/dy} requires the availability of
y
F(x, y) and the partial derivatives of the other functions defining the setR(x, y) with respect to the parametersy.Research sponsored by National Science Foundation Grant ECS-8709795 and Office of Naval Research Contract N00014-89-J-1537. We thank the referees for constructive comments on an earlier version of this paper. 相似文献
8.
Hecke groups H(q) are the discrete subgroups of
generated by S(z) = –(z+ q)–1and T(z) = –1/z. The commutator subgroup of H(q), denoted by H(q), is studied in [2]. It was shown that H(q) is a free group of rank q– 1.Here the extended Hecke groups
obtained by adjoining
to the generators of H(q) are considered. The commutator subgroup of
is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the H(q) case, the index of H(q) is changed by q, in the case of
this number is either 4 for qodd or 8 for qeven. 相似文献
9.
Consider the problem of determining the roots of an equation of the formF() =0 whereF maps the Banach spaceX into itself. Convergence theorems for the iterative solution ofF() =0 are proved for multipoint algorithms of the form
n+1=
n
-
(
n
), 1, where
and 0()=0. The theorems are applied to the solution of two point boundary value problems of the form
=f
(y, t), g(y(0))+h(y(1))=c. A set {A(t),B,C} of matrices is called boundary compatible if the linear two point boundary value problem
=A(t)) y+k (t),B y (0) + C y (1) = d has a unique solution for allk (t) andd. Then, under certain conditions, there are boundary compatible sets such that the problem
=f (y, t),g (y (0) ) +h (y (1)) =c has the equivalent integral representation where and are Green's matrices for the linear problem
=A(t)y +k(t),B y (0) +C y (1) =d. Eq. (i) is viewed as an operator equation of the formF (x) =(I-T) (x) = 0 and convergence conditions for the iterative solution of (i) are deduced from the general theorems. Explicit interpretations of the convergence results are given in terms off, g, h and some illustrative numerical examples are presented.This research has been supported by the National Aeronautics and Space Administration under Grant No. NGR-40-002-015.This research has been supported by the National Science Foundation under Grant No. GK-2788. 相似文献
10.
P. G. Grinevich 《Theoretical and Mathematical Physics》1994,99(2):599-605
The direct and the inverse scattering problems for the heat-conductivity operator
are studied for the following class of potentials:u(x,y)=u
o
(x,y)+u
1(x,y), whereu
o
(x,y) is a nonsingular real finite-gap potential andu
1(x,y) decays sufficiently fast asx
2+y2. We show that the scattering data for such potentials is the
data on the Riemann surface corresponding to the potentialu
o
(x,y). The scattering data corresponding to real potentials is characterized and it is proved that the inverse problem corresponding to such data has a unique nonsingular solution without the small norm assumption. Analogs of these results for the fixed negative energy scattering problem for the two-dimensional time-independent Schrödinger operator
are obtained.L. D. Landau Institute for Theoretical Physics, Kosygina 2, GSP-1, Moscow 177940, Russia. E-mail: pgg@cpd.landau.free.net. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 300–308, May, 1994. 相似文献
11.
Let be a bounded domain in #x211D;n with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem:
12.
Summary.
Let
be a field of real or complex numbers and
denote the set of nonzero elements of
.
Let
be an abelian group. In this paper, we solve the functional equation
f
1
(x +
y) +
f
2
(x -
y) =
f
3
(x) +
f
4
(y) +
g(xy)
by modifying the domain of the unknown functions
f
3,
f
4, and
g from
to
and using a method different from [3]. Using this result,
we determine all functions
f
defined on
and taking values on
such that the difference
f(x + y) + f
(x -
y) - 2
f(x) - 2
f(y)
depends only on the product
xy for all
x and
y in
相似文献
13.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind
and
where
is a singular Volterra operator,
is continuous and positive on ]a, b],
is a norm in R
n, and [u]+ and [u]– are respectively the positive and the negative part of the vector u R
n. 相似文献
14.
Pei Hsu 《Probability Theory and Related Fields》1990,84(1):103-118
We study properties of Brownian bridges on a complete Riemannian manifoldM. LetQ
x,y
t
be the law of Brownian bridge fromx toy with lifetimet. Q
x,y
t
is a probability measure on the space
x,y
of continuous paths with (0)=x and (1)=y. We prove thatQ
x,y
t
possesses the large deviation property with the rate function
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