共查询到20条相似文献,搜索用时 937 毫秒
1.
《Mathematical and Computer Modelling》1997,25(3):69-79
Some necessary conditions are established for the nonoscillation of solutions of the second-order neutral delay differential equation [a(t)(x (t) + p(t)x(t − τ)′]′ + q(t)f(x(t − σ)) = 0. Using these results, we obtain some oscillation criteria for the above equation. 相似文献
2.
《Journal of Mathematical Analysis and Applications》1987,124(1):213-224
Some oscillation criteria are established for certain second order nonlinear differential equations of the form (a(t)ψ(x(t)) x. (t)). + p(t) x. (t) + q(t)f(x(t)) = 0. These criteria improve upon some of the known results by Kura, Kamenev and Philos. 相似文献
3.
Mustafa Hasanbulli 《Applied mathematics and computation》2010,215(12):4392-4399
By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form
(r(t)(x(t)+p(t)x(t-τ))′)′+q(t)f(x(t),x(σ(t)))=0. 相似文献
4.
Amy Del Medico 《Journal of Mathematical Analysis and Applications》2004,294(2):621-643
We establish Kamenev-type criteria and interval criteria for oscillation of the second-order scalar differential equation (p(t)xΔ(t))Δ+q(t)x(σ(t))=0 on a measure chain. Our results cover those for differential equations and provide new oscillation criteria for difference equations. Several examples are given to show the significance of the results. 相似文献
5.
《Mathematical and Computer Modelling》2000,31(2-3):17-29
In this paper, we consider the partial difference equation with continuous variables of the form P1z(x + a, y + b) + p2z (x + a, y) + p3z (x, y + b) − p4z (x, y) + P (x, y) z (x − τ, y − σ) = 0, where P ϵ C(R+ × R+, R+ − {0}), a, b, τ, σ are real numbers and pi (i = 1, 2, 3, 4) are nonnegative constants. Some sufficient conditions for all solutions of this equation to be oscillatory are obtained. 相似文献
6.
Zhaowen Zheng 《Acta Mathematica Hungarica》2006,110(3):241-252
Summary Using the integral average method, we give some new oscillation criteria for the second order differential equation with damped
term (a(t)Ψ(x(t))K(x'(t)))'+p(t)K(x'(t))+q(t)f(x(t))=0, t<span style='font-size:10.0pt; font-family:"Lucida Sans Unicode"'>≧t0. These results improve and generalize the oscillation criteria in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1],
because they eliminate both the differentiability of p(t) and the sign of p(t), q(t). As a consequence, improvements of Sobol's type oscillation criteria are obtained. 相似文献
7.
Qing-Hai HaoFang Lu 《Applied mathematics and computation》2011,217(17):7126-7131
In this paper, we are concerned with the oscillation of second order superlinear differential equations of the form
(a(t)y′(t))′+p(t)y′(t)+q(t)f(y(t))=0. 相似文献
8.
We obtain some oscillation criteria for solutions to the nonlinear dynamic equation
xΔΔ+q(t)xΔσ+p(t)(f○xσ)=0, 相似文献
9.
R.E White 《Journal of Mathematical Analysis and Applications》1979,68(1):157-170
We consider weak solutions to the nonlinear boundary value problem (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0)) u′(0) = ku(0), r(L, u(L)) u′(L) = hu(L) and k, h are suitable elements of [0, ∞]. In addition to studying some new boundary conditions, we also relax the constraints on r(x, u) and (Fu)(x). r(x, u) > 0 may have a countable set of jump discontinuities in u and r(x, u)?1?Lq((0, L) × (0, p)). F is an operator from a suitable set of functions to a subset of Lp(0, L) which have nonnegative values. F includes, among others, examples of the form (Fu)(x) = (1 ? H(x ? x0)) u(x0), (Fu)(x) = ∫xLf(y, u(y)) dy where f(y, u) may have a countable set of jump discontinuities in u or F may be chosen so that (Fu)′(x) = ? g(x, u(x)) u′(x) ? q(x) u(x) ? f(x, u(x)) where q is a distributional derivative of an L2(0, L) function. 相似文献
10.
Zhiting Xu 《Monatshefte für Mathematik》2007,57(5):157-171
Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation
of Emden-Fowler type
(a(t)x¢(t))¢+q1(t)| y(t-s1)|a sgn y(t-s1) +q2(t)| y(t-s2)|b sgn y(t-s2)=0, t 3 t0,(a(t)x'(t))'+q_1(t)| y(t-\sigma_1)|^{\alpha}\,{\rm sgn}\,y(t-\sigma_1) +q_2(t)| y(t-\sigma_2)|^{\beta}\,{\rm sgn}\,y(t-\sigma_2)=0,\quad t \ge t_0,
where x(t) = y(t) + p(t)y(t − τ), τ, σ1 and σ2 are nonnegative constants, α > 0, β > 0, and a, p, q
1,
q2 ? C([t0, ¥), \Bbb R)q_2\in C([t_0, \infty), {\Bbb R})
. The results of this paper extend and improve some known results. In particular, two interesting examples that point out
the importance of our theorems are also included. 相似文献
11.
Frederick Bloom 《Journal of Mathematical Analysis and Applications》1983,96(2):551-583
Initial boundary value problems for the damped nonlinear wave equation wtt = σ(w)xx ? ywt arise in several areas of applied mathematics and, in particular, in studies of shearing flow in a nonlinear viscoelastic fluid; the problems of global existence and nonexistence of smooth solutions have been extensively studied in the strictly hyperbolic case σ′(δ) ? ε > 0, ?δ?R1 as well as in the case where σ′(0) > 0 and the initial data are chosen so small that σ′(w) > 0 for as long as a smooth solution w(x, t) exists. In this paper the global nonexistence problem is studied for the cases σ′(0) = 0 and σ′(0) > 0 but σ′(δ) < 0 for ¦δ¦ sufficiently large and growth estimates which are valid on the maximal interval of existence of a sufficiently smooth solution are derived. 相似文献
12.
Sun-Wah Kiu 《Stochastic Processes and their Applications》1980,10(2):183-191
A Markov process in Rn{xt} with transition function Pt is called semi-stable of order α>0 if for every a>0, Pt(x, E) = Pat(aax, aaE). Let ?t(ω)=∫t0|xs(ω)|-1/α ds, T(t) be its inverse and {yt}={xT(t)}.Theorem 1: {Yt} is a multiplicative invariant process; i.e., it has transition function qt satisfying qt(x,E)=qt(ax,aE) for all a > 0.Theorem 2: If {xt} is Feller, right continuous and uniformly stochastic continuous on a neighborhood of the origin, then {yt} is Feller. 相似文献
13.
New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping 总被引:1,自引:0,他引:1
Yuan Gong Sun 《Journal of Mathematical Analysis and Applications》2004,291(1):341-351
Some new oscillation criteria are established for the nonlinear damped differential equation (r(t)y′)′+p(t)y′+q(t)f(y)=0 that are different from most known ones in the sense that they are based on a class of new functions Φ(t,s,r) defined in the sequel. Our results are sharper than some previous results which can be seen by the examples at the end of this paper. 相似文献
14.
In this paper we establish existence-uniqueness of solution of a class of singular boundary value problem −(p(x)y′′(x))=q(x)f(x,y) for 0<x?b and y(0)=a, α1y(b)+β1y′(b)=γ1, where p(x) satisfies (i) p(x)>0 in (0,b), (ii) p(x)∈C1(0,r), and for some r>b, (iii) is analytic in and q(x) satisfies (i) q(x)>0 in (0,b), (ii) q(x)∈L1(0,b) and for some r>b, (iii) is analytic in with quite general conditions on f(x,y). Region for multiple solutions have also been determined. 相似文献
15.
Anna Maria Mantero 《Journal of Functional Analysis》1982,47(1):7-25
Let K be a distribution on 2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∝∝ dudvK(x ? u, y ? v) f(u, v) exp(ixv ? iyu). We show that there exists K such that the operator λ(K) is bounded on Lp(R)2 for every p in (1, 2¦, but is unbounded on Lq(R)2 for every q > 2. 相似文献
16.
Explosive solutions of elliptic equations with absorption and nonlinear gradient term 总被引:2,自引:0,他引:2
Marius Ghergu Constantin Niculescu Vicenţiu Rădulescu 《Proceedings Mathematical Sciences》2002,112(3):441-451
Letf be a non-decreasing C1-function such that
andF(t)/f
2
a(t)→ 0 ast → ∞, whereF(t)=∫
0
t
f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|
a
=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded. 相似文献
17.
In this paper, a higher order p-Laplacian neutral functional differential equation with a deviating argument:
[φp([x(t)−c(t)x(t−σ)](n))](m)+f(x(t))x′(t)+g(t,x(t−τ(t)))=e(t) 相似文献
18.
J. Knežević-Miljanović 《Differential Equations》2009,45(2):267-270
We consider the equation y″ = P(x)x a y σ , σ < 0, and prove the unique solvability of the Cauchy problem y(0) = 0, y′(0) = λ. 相似文献
19.
Chen Xiuhong 《Journal of Mathematical Analysis and Applications》2002,267(1):377-394
In this paper, a class of multiobjective control problems is considered, where the objective and constraint functions involved are f(t, x(t), ?(t), y(t), z(t)) with x(t) ∈ Rn, y(t) ∈ Rn, and z(t) ∈ Rm, where x(t) and z(t) are the control variables and y(t) is the state variable. Under the assumption of invexity and its generalization, duality theorems are proved through a parametric approach to related properly efficient solutions of the primal and dual problems. 相似文献
20.
In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation
(r(t)((y(t)+p(t)y(t−τ)Δ)γ)Δ)+f(t,y(t−δ))=0 相似文献