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1.
Summary We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations.
These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations
and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous.
We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential
equation of the general form (|x'|α-1x')' + a(t) |x|α-1x = 0. 相似文献
2.
Sufficient conditions are established for the oscillation of even order neutral differential equations of the formwhere n 2 is even integer. 相似文献
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4.
Martin Bohner Said R. Grace Irena Jadlovská 《Mathematical Methods in the Applied Sciences》2020,43(17):10041-10053
This paper is a continuation of a recent work by the authors on the oscillatory properties of second-order half-linear neutral delay differential equations. Providing a new apriori bound for a nonoscillatory solution, we present a new oscillation criterion, which essentially improves the existing ones. In a particular nonneutral case, the obtained oscillation constant is unimprovable. 相似文献
5.
通过运用分析方法,对微分不等式进行估计,得到了一类偶数阶半线性微分方程解的振动性的若干判别准则.所得结果减弱了已有文献的条件,推广和改进了已有文献的结果. 相似文献
6.
J. Sugie 《Acta Mathematica Hungarica》2008,118(4):369-394
This paper deals with the second-order half-linear differential equation
Here ϕ
p
(z):= |z|
p−2
z is the so-called one-dimensional p-Laplacian operator. Our main purpose is to establish new criteria for all nontrivial solutions to be oscillatory and for
those to be nonoscillatory. In our theorems, the parametric curve given by (a(t), b(t)) plays a critical role in judging whether all solutions are oscillatory or nonoscillatory. This paper takes a di-erent approach
from most of the previous research. Our results are new even in the linear case (p = 2). The method used here is mainly phase plane analysis for a system equivalent to the half-linear differential equation.
Some suitable examples are included to illustrate the main results. Global phase portraits are also attached.
Supported in part by Grant-in-Aid for Scientific Research 19540182. 相似文献
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Ordinary differential equations in the oscillation theory of partial half-linear differential equation 总被引:1,自引:0,他引:1
Robert Ma?ík 《Journal of Mathematical Analysis and Applications》2008,338(1):194-208
In the paper we study the damped half-linear partial differential equation
9.
Interval criteria for oscillation of second-order half-linear differential equations 总被引:1,自引:0,他引:1
By employing a generalized Riccati technique and an integral averaging method, interval oscillation criteria are established for the second-order half-linear differential equation [r(t)|x′(t)|α−1x′(t)]′+q(t)|x(t)|α−1x(t)=0. These criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line. They also extend, improve, and complement a number of existing results, and can be applied to extreme cases such as . In particular, several interesting examples that illustrate the importance of our results are included. 相似文献
10.
By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system
(P(t)X'(t))' + R(t)X'(t) + Q(t)X(t) =0, t ≥ to 〉 0
where P(t), R(t), Q(t) are n × n real continuous matrix functions, P(t) and R(t) are commutative. Theresults improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper. 相似文献
(P(t)X'(t))' + R(t)X'(t) + Q(t)X(t) =0, t ≥ to 〉 0
where P(t), R(t), Q(t) are n × n real continuous matrix functions, P(t) and R(t) are commutative. Theresults improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper. 相似文献
11.
Ondřej Došlý 《Czechoslovak Mathematical Journal》2000,50(3):657-671
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
12.
O. Dosly J. R. Graef J. Jaros 《Proceedings of the American Mathematical Society》2003,131(9):2859-2867
Oscillation properties of solutions of the forced second order linear difference equation
are investigated. The authors show that if the forcing term does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-linear equation
are also given.
are investigated. The authors show that if the forcing term does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-linear equation
1, \end{displaymath}">
are also given.
13.
Oscillation theorems for second-order half-linear differential equations 总被引:11,自引:0,他引:11
Oscillation criteria for the second-order half-linear differential equation are established, where > 0 is a constant and
exists for t [t0, ∞). We apply these results to the following equation: where
, D = (D1,…, DN), Ωa = x
N : |x| ≥ a} is an exterior domain, and c C([a, ∞),
), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant. 相似文献
[r(t)|ξ′(t)|−1 ξ′(t)]′ + p(t)|ξ(t)|−1ξ(t)=0, t t0
14.
Kamenev-type oscillation criteria for delay difference equations 总被引:2,自引:0,他引:2
程金发 《数学物理学报(B辑英文版)》2007,27(3):574-580
Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation Δ(pn(Δ(xn cnxn-τ))γ) qnxβn-σ=0,n=0,1,2…which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10]. 相似文献
15.
Some new oscillation criteria are established for the second-order matrix differential system(r(t)Z′(t))′ p(t)Z′(t) Q(t)F(Z′(t))G(Z(t)) = 0, t ≥ to > 0,are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. The results weaken the condition of Q(t) and generalize some well-known results of Wong (1999) to nonlinear matrix differential equation. 相似文献
16.
The purpose of this paper is to provide an oscillation theorem that can be applied to half-linear differential equations with time-varying coefficients. A parametric curve by the coefficients is focused in order to obtain our theorem. This parametric curve is a generalization of the curve given by the characteristic equation of the second-order linear differential equation with constant coefficients. The obtained theorem is proved by transforming the half-linear differential equation to a standard polar coordinates system and using phase plane analysis carefully. 相似文献
17.
Qingkai Kong 《Journal of Mathematical Analysis and Applications》2007,332(1):512-522
We study the oscillation problems for the second order half-linear differential equation ′[p(t)Φ(x′)]+q(t)Φ(x)=0, where Φ(u)=|u|r−1u with r>0, 1/p and q are locally integrable on R+; p>0, q?0 a.e. on R+, and . We establish new criteria for this equation to be nonoscillatory and oscillatory, respectively. When p≡1, our results are complete extensions of work by Huang [C. Huang, Oscillation and nonoscillation for second order linear differential equations, J. Math. Anal. Appl. 210 (1997) 712-723] and by Wong [J.S.W. Wong, Remarks on a paper of C. Huang, J. Math. Anal. Appl. 291 (2004) 180-188] on linear equations to the half-linear case for all r>0. These results provide corrections to the wrongly established results in [J. Jiang, Oscillation and nonoscillation for second order quasilinear differential equations, Math. Sci. Res. Hot-Line 4 (6) (2000) 39-47] on nonoscillation when 0<r<1 and on oscillation when r>1. The approach in this paper can also be used to fully extend Elbert's criteria on linear equations to half-linear equations which will cover and improve a partial extension by Yang [X. Yang, Oscillation/nonoscillation criteria for quasilinear differential equations, J. Math. Anal. Appl. 298 (2004) 363-373]. 相似文献
18.
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
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林文贤 《纯粹数学与应用数学》2007,23(4):467-470
讨论了一类偶数阶中立型偏泛函微分方程系统在Robin边界条件下解的振动性,获得了所有解振动的若干充分条件,同时也给出了实际应用例子. 相似文献