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

3.
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   

4.
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   

5.
We prove the existence of continuously differentiable solutions such that
or
where
  相似文献   

6.
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   

7.
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   

8.
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   

9.
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   

10.
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation
of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution y(x) which behaves in this way.  相似文献   

11.
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   

12.
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
  相似文献   

13.
Consider the forced higher-order nonlinear neutral functional differential equation
where n,m , 1 are integers, , i + = [0,), C,Q i, g C([t 0,), ), fi C(, ), (i = 1, 2, ...;, m). Some sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general Q i(t) (i = 1, 2, ... ,m) and g(t) which means that we allow oscillatory Qi(t) (i = 1, 2, ... ,m) and g(t). Our results improve essentially some known results in the references.Project was supported by the Special Funds for Major State Basic Research Projects (G19990328) and Hunan Natural Science Foundation of P.R. China (10371103).  相似文献   

14.
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   

15.
In this paper, we are concerned with the global behavior ofthe solutions of the difference equation
where
and . Necessary and sufficient conditions for boundedness, persistence,and periodicity of all solutions will be established. The oscillatorybehavior will be investigated.  相似文献   

16.
There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let ϕ (t) be a scalar continuous monotonically increasing positive function tending to ∞ as t → ∞. It is established that if all solutions of a differential system satisfy the inequality
then the solution x(t; t 0, x 0) of this differential system tends to 0 faster than .__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 137–142, January, 2005.  相似文献   

17.
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   

18.
LetL(x, t) be the local time process of a standard Wiener process {W(t),t>0}. Denote
  相似文献   

19.
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   

20.
We consider the parabolic SPDE
with the Neuman boundary condition
and some initial condition.We use the Malliavin calculus in order to prove that, if the coefficients and are smooth and > 0, then the law of any vector (X(t,x1),..., X(t,xd)), 0 x1 ... xd 1, has a smooth, strictly positive density with respect to Lebesgue measure.  相似文献   

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