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1.
We consider the boundary-value problem
where and n is the unit outward normal. We show that there exist so many nonequivalent positive weak solutions as prescribed under certain conditions on q and R. We construct nonradial solutions for [(n + 1)/2] + 1 ⩽ p < n and some q. Bibliography: 18 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 121–144.  相似文献   

2.
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign.  相似文献   

3.
Using the integral operator that defines a solution of the Cauchy problem for the equation
we find an integral representation for solutions of the equation
in terms of arbitrary functions that are continuously differentiable sufficiently many times.  相似文献   

4.
In this paper we prove the existence of at least one positive solution of the equation
  相似文献   

5.
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   

6.
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   

7.
We prove the existence of continuously differentiable solutions such that
or
where
  相似文献   

8.
We study oscillatory properties of the second order half-linear difference equation
. It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation
. We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.  相似文献   

9.
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   

10.
The following classes of functions analytic in the unit disk are considered:
and
where is the Nevanlinna characteristic and is a properly changing positive function on (0,1]. Necessary and sufficient conditions on are established under which the classes and are invariant under the operators of differentiation and integration. Bibliography: 7 titles.  相似文献   

11.
We study the conditions for the existence and nonexistence of global in time (t > 0), nonnegative solutions of the problem
0,$$ " align="middle" vspace="20%" border="0">
1,\quad q > 0.$$ " align="middle" vspace="20%" border="0">
If p + q ≤ 2 + 2/N, then the problem has no global nontrivial solutions. If p + q > 2 + 2/N, then such solutions exist. Some generalizations of this problem are discussed.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.  相似文献   

12.
We study the problem of asymptotic integration of the linear integro-differential equation
, and the achievement of an asymptotic formula for the solutions of the equation
.  相似文献   

13.
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   

14.
When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation
is considered. Sufficient conditions concerning f are formulated in order to guarantee the existence of a positive solution for k . An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results hold only for delayed equations (i.e. for n > 0) and not for the case of an ordinary equation (with n = 0).  相似文献   

15.
Some new criteria for the oscillation of difference equations of the form
and
are established.  相似文献   

16.
Rhouma  N. Belhaj  Mosbah  M. 《Potential Analysis》2004,21(2):137-150
In this paper, we consider a problem of the form
where d3, f is a positive locally Lipschitz bounded function and g is assumed to change sign. We give some conditions of integral type to get the existence of positive solutions for large enough.  相似文献   

17.
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   

18.
For entire Dirichlet series of the form , we establish conditions under which the relation
holds uniformly in outside a certain set E for which
where h() is a positive continuous function increasing to + on [0, +).  相似文献   

19.
Let , and let be Epstein's zeta-function of the form Q. It is proved that for |t| > C > 0 one has the estimate
Bibliography: 9 titles.  相似文献   

20.
We state a maximum principle for the gradient of the minima of integral functionals
just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.  相似文献   

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