On oscillation of nonlinear second-order differential equations with damping term
نویسندگان
چکیده
منابع مشابه
Oscillation of Second-order Nonlinear Differential Equations with Damping
We study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results. c ©2014 Mathematical ...
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Some oscillation criteria for solutions of a general ordinary differential equation of second order of the form (r(t)ψ(x(t))ẋ(t))+h(t)ẋ(t)+q(t)φ(g(x(t)),r(t)ψ(x(t))ẋ(t)) = H(t,x(t), ẋ(t)) with alternating coefficients are discussed. Our results improve and extend some existing results in the literature. Some illustrative examples are given with its numerical solutions which are computed using R...
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A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.
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This paper concerns the oscillation of solutions to the differential equation ` r(t)x′(t) ́′ + p(t)x′(t) + q(t)g(x(t)) = 0, where xg(x) > 0 for all x 6= 0, r(t) > 0 for t ≥ t0 > 0. No sign conditions are imposed on p(t) and q(t). Our results solve the open problem posed by Rogovchenko [27], complement the results in Sun [29], and improve a number of existing oscillation criteria. Our main resul...
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and Applied Analysis 3 Proof. Assume that 1.1 has a nonoscillatory solution x t . Without loss of generality, suppose that it is an eventually positive solution if it is an eventually negative solution, the proof is similar , that is, x t > 0 for all t ≥ t0. We consider the following three cases. Case 1. Suppose that x′ t is oscillatory. Then there exists t1 ≥ t0 such that x′ t1 0. From 1.1 , w...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.05.029