共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations. 相似文献
2.
In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. 相似文献
3.
In this paper, we give a generalization of the well-known Lyapunov-type inequality for a class of odd-order differential equations, the result of this paper is new and generalizes some early results on this topic. 相似文献
4.
In this paper, we sketch some recent developments in the theory of Lyapunov-type inequalities and present some new results relating to a quasilinear system, special cases of which contain some well-known differential equations such as half-linear and linear equations. Our result generalize the Lyapunov-type inequality given in [18]. 相似文献
5.
Antonio Cañada Juan A. Montero Salvador Villegas 《Mediterranean Journal of Mathematics》2006,3(2):177-187
Let us consider the linear boundary value problem
where
and
is defined by
Classical Lyapunov inequality states that
for any function
where
The constant 4/L is optimal. Let us note that Lyapunov inequality is given in terms of
the usual norm in the space L1(0, L). In this paper we review some recent results on Lp Lyapunovtype inequalities,
, for ordinary and partial differential equations on a bounded and regular domain in
In the last case, it is showed that the relation between the quantities p and N/2 plays a crucial role, pointing out a deep difference with respect to the ordinary case. In the proof, the best constants
are obtained by using a related variational problem and Lagrange multiplier theorem. Finally, the linear results are combined
with Schauder fixed point theorem in the study of resonant nonlinear problems.
The authors have been supported by the Ministry of Science and Technology of Spain MTM2005- 01331 and by Junta de Andalucia
(FQM116). 相似文献
((0.1)) |
6.
In this paper, we generalize the well-known Lyapunov-type inequality for second-order linear differential equations to a class of even-order linear differential equations, the results of this paper are new and generalize some known inequalities in the literatures. 相似文献
7.
Jiayong WU 《数学年刊B辑(英文版)》2020,41(2):267-284
This paper deals with constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ωt = ?ω + aωln ω on closed manifolds. A new interpolated Harnack inequality for ωt = ?ω-ωln ω +εRω on closed surfaces under ε-Ricci flow is also derived. Finally, the author proves a new differential Harnack inequality for ωt= ?ω-ωln ω under Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions,... 相似文献
8.
考虑带有非线性阻尼项的一类二阶微分方程的振动性质.在一般的假设下我们建立了这类方程的若干新的振动准则.所得结果推广和改进了文献中的某些结果. 相似文献
9.
10.
本文利用Riccati技巧和平均技巧,研究一类二阶非线性微分方程的振动性,得到了这类方程振动的若干新的判别准则。 相似文献
11.
Lyapunov-type inequalities are estimated to give necessary conditions for the existence of positive solutions for several types of scalar equations and systems of one-dimensional Minkowski-curvature problems with singular weights. 相似文献
12.
13.
给出了一类三阶非线性微分方程存在非振荡解的充分条件,使得Parhi准则更加一般化。在一些特殊情况下,这些结论适合于更弱的条件。 相似文献
14.
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' p(t)(y'(t))σ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results. 相似文献
15.
n阶非线性常微分方程的非线性两点边值问题 总被引:1,自引:1,他引:0
本文利用打靶法,给出了n阶非线性常微分方程具有非线性两点边界条件的边值问题存在解与存在唯一解的一般性结果,并将所得结果应用于Lipschitz方程的两点过值问题,给出了存在解与存在唯一解的具体的充分条件。 相似文献
16.
利用Ho lder不等式研究一类非线性项具时滞的二阶中立型时滞微分方程{r(t)[y(t)+p(t)y(t-τ)]′2m+1}′+q(t)f[y(t-σ)]=0(t>t0)的振动性.给出了该方程的解振动的若干充分条件,所得结果推广了已有的相应结论. 相似文献
17.
18.
19.
E.M. Elabbasy 《数学研究及应用》1995,15(3):329-336
Conditions are given on the hunctions f, g, h,p and q which imply that allcontinuable solutions of are abounded as well as oscillatory on the interval [t0,∞), t0> 0. 相似文献
20.
E.M. Elabbasy 《数学研究与评论》1995,(3)
OscillationofSolutionsforaSecondOrderNonlinearPerturbedDifferentialEquationswithFunctionalArgumentsE.M.Elabbasy(Dept.ofMath.,... 相似文献