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1.
The purpose of this paper is to obtain oscillation criteria for the differential system
  相似文献   

2.
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   

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

4.
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   

5.
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   

6.
In this paper we establish the existence of nontrivial solutions to
with V x superlinear in x.  相似文献   

7.
Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation
in a random semi-Markov medium described by an ergodic semi-Markov process x(t).Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 713–720, May, 2004.  相似文献   

8.
Determinants of Matrices Associated with Incidence Functions on Posets   总被引:3,自引:1,他引:2  
Let S = x 1,...,x n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let denote the n × n matrix having f evaluated at the meet of x i and x j as its i, j-entry and denote the n × n matrix having f evaluated at the join of x i and x j as its i, j-entry. The set S is said to be meet-closed if for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices and on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications.  相似文献   

9.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
0,$$ " align="middle" vspace="20%" border="0">
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   

10.
In this paper we investigate commutativity of rings with unity satisfying any one of the properties:
for some f(X) in and g(X), h(X) in where m 0, r 0, s 0, n > 0, t > 0 are non-negative integers. We also extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values. Further, under different appropriate constraints on commutators, commutativity of rings has been studied. These results generalize a number of commutativity theorems established recently.  相似文献   

11.
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   

12.
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   

13.
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   

14.
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   

15.
By the Fourier method a solution of the equation
  相似文献   

16.
In this paper we investigate oscillatory properties of the second order half-linear equation
Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.  相似文献   

17.
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   

18.
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   

19.
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   

20.
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   

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