Periodic solutions for nonlinear nth order differential equations with delays
نویسندگان
چکیده
منابع مشابه
ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *
The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
متن کاملon the periodic solutions of a class of nth order nonlinear differential equations *
the nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. using the leray-schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
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and Applied Analysis 3 Now, let f̃ : R 1 → R be a continuous function, T -periodic with respect to the first variable, and consider the nth-order differential equation u n f̃ ( t, u, u′, u′′, . . . , u n−1 ) . 2.5 Lemma 2.1 see 14 . Assume that the following conditions hold. i There exists ρ > 0 such that, for each λ ∈ 0, 1 , one has that any possible T -periodic solution u of the problem u n λf̃ ...
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* Correspondence: [email protected] School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, P. R. China Full list of author information is available at the end of the article Abstract By using the critical point theory and S index theory, we obtain a new result for the existence and multiplicity of periodic solutions for a class of second-order...
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Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L0y, . . . , Ln−1y) under the validity of the sign condition f(t, x1, . . . , xn)x1 ≤ 0, f(t, 0, x2, . . . , xn) = 0 on R+ × Rn.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.04.029