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James S. W. Wong 《Proceedings of the American Mathematical Society》1999,127(5):1387-1395
We prove nonoscillation theorems for the second order Emden-Fowler equation (E): , , where and . It is shown that when is nondecreasing for any and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when and .
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E.M.E. Zayed M.A. El-Moneam 《数学物理学报(B辑英文版)》2007,27(3):602-610
The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) > 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable. 相似文献
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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
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Timothy A. Ademola 《Applied mathematics and computation》2010,216(10):3044-3049
Sufficient conditions for the existence of solutions to boundedness and ultimate boundedness problems associated to a certain third order nonlinear differential equation are given by means of the Lyapunov’s second method. The appropriate Lyapunov function is given explicitly. Our results complement some well known results on the third order differential equations in the literature. 相似文献
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In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of nonlinear third order difference equations of the form
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Yaojun Ye 《Applicable analysis》2013,92(11):2424-2437
We consider the initial-boundary value problem for a class of nonlinear hyperbolic equations system in a bounded domain. Using the potential well theory, the existence of global solutions is investigated. We also established the asymptotic behaviour of global solutions as t?→?+?∞ by applying the multiplier method. 相似文献
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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
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Oscillatory and asymptotic criteria of third order nonlinear delay dynamic equations with damping term on time scales
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Qinghua Feng 《Journal of Applied Analysis & Computation》2018,8(4):1260-1281
In this paper, we are concerned with oscillatory and asymptotic behavior of third order nonlinear delay dynamic equations with damping term on time scales. By using a generalized Riccati function and inequality technique, we establish some new oscillatory and asymptotic criteria. The established results on one hand extend some known results in the literature, on the other hand unify continuous and discrete analysis as two special cases of an arbitrary time scale. We also present some applications for the established results. 相似文献
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Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations
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T. Candan 《Mathematical Methods in the Applied Sciences》2015,38(7):1379-1392
The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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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
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中立型二阶非线性微分方程振动性的判据 总被引:7,自引:0,他引:7
Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms: 相似文献
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通过建立几个微分不等式将经典的微分方程零点比较定理推广到二阶非线性微分方程,得到若干新的结论. 相似文献
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This paper is concerned with nonoscillatory solutions of the fourth order quasilinear differential equation
where α > 0, β > 0 and p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0 (t≥a). The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions
are established for the existence of nonoscillatory solutions having specific asymptotic growths as t→∞.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Tadeusz Jankowski 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(2):913-923
We use a fixed point theorem due to Avery and Peterson to establish the existence of at least three non-negative solutions of some nonlocal boundary value problems to third order differential equations with advanced arguments. An example is given to illustrate the main results. 相似文献