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1.
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   

2.
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$$ " align="middle" border="0"> and 0$$ " align="middle" border="0"> , 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   

3.
We prove the existence of continuously differentiable solutions such that
or
where
  相似文献   

4.
Dedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator
in a noncylindrical domain . We obtain local solution in t. When we add a viscosity we obtain a global solution. We also investigate the asymptotic behavior of the energy.  相似文献   

5.
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   

6.
We consider parabolic variational inequalities having the strong formulation
((1))
where for some admissible initial datum, V is a separable Banach space with separable dual is an appropriate monotone operator, and is a convex, lower semicontinuous functional. Well-posedness of (1) follows from an explicit construction of the related semigroup Illustrative applications to free boundary problems and to parabolic problems in Orlicz-Sobolev spaces are given.  相似文献   

7.
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
be the Fejér kernel, C be the space of contiuous 2π-periodic functions f with the norm , let
be the Jackson polynomials of the function f, and let
be the Fejér sums of f. The paper presents upper bounds for certain quantities like
which are exact in order for every function fC. Special attention is paid to the constants occurring in the inequalities obtained. Bibliography: 14 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 90–114.  相似文献   

9.
In this work the authors study the conditions for the existence of diffusion equations
in the cylinder Q = 3D × +, n , satisfying the homogeneous Dirichlet or Neumann conditions on the side boundary of the cylinder Q and decreasing with respect to t as a power for t .  相似文献   

10.
By the Fourier method a solution of the equation
  相似文献   

11.
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   

12.
Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation
and determine the general form of a solution by using zeros of an entire function A 2(z) of exponential type.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 695–704, May, 2004.  相似文献   

13.
In this paper we establish the existence of nontrivial solutions to
with V x superlinear in x.  相似文献   

14.
具时滞的奇异(n-1,1)共轭边值问题的多重正解   总被引:2,自引:0,他引:2  
Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones  相似文献   

15.
We consider the optimization of the two-dimensional transformation of the spatial arguments of the sought function in the mixed initial boundary-value problem for the functional-differential diffusion equation
where the right-hand side is defined by the generalized superposition , and the argument transformation g(x) in the form of the functional
defined on the space of continuous test functions . The quality of optimization is evaluated by the integral functional
The minimizing sequence for the minimization problem J(g) inf G on the set G = g L 2(Q): g ( ) } of pointwise-bounded transformations is constructed by the gradient projection method combined with special projection-difference approximations of the direct and the conjugate initial boundary-value problems, which allow for possible irreversibility of the argument transformation and its generalized specification. Numerical optimization results are discussed using two examples of localized objective functions u 1(x, t).  相似文献   

16.
Let be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators generated by a multiplier matrix defined by the following relations:
and
In the case || = || = 1/2, we prove the following statements for the Jacobi polynomials (these statements are similar to known results for the trigonometrical system). Consider the cases
and
Under some conditions on a function , the values and equal
and
In addition, we show that for the Fourier–Legendre summation methods ( = = 0) generated by the multiplier function , the limit and supremum of the sequence of Lebesgue constants may differ. Bibliography: 11 titles.  相似文献   

17.
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   

18.
We study a new type of solutions to differential inclusions in Banach spaces, which we call directional solutions. The idea is based on the observation that for a differentiable function and a closed set
The above formula, which ‘makes sense’ also for non-differentiable functions, allows us to investigate nowhere differentiable solutions to differential inclusions. Thus we say that is a directional solution to if
We show that directional solutions have better properties than classical ones, in particular a limit of a convergent sequence of approximate solutions is an exact solution. We also prove that is a directional solution to if
  相似文献   

19.
20.
A Littlewood-Paley type inequality   总被引:2,自引:0,他引:2  
In this note we prove the following theorem: Let u be a harmonic function in the unit ball and . Then there is a constant C = C(p, n) such that
.  相似文献   

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