Existence of periodic solution for a higher-order p-Laplacian differential equation with multiple deviating arguments

2020;
: pp. 420–428
https://doi.org/10.23939/mmc2020.02.420
Received: July 04, 2020
Accepted: October 03, 2020

Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 420–428 (2020)

1
Department of Mathematics, Multidisciplinary Faculty, Mohammed first University of Oujda
2
Department of Mathematics, Faculty of Sciences, Mohammed first University of Oujda

By applying Mawhin's continuation theorem, theory of Fourier series, Bernoulli numbers theory and some new inequalities, we study the higher-order $p$-Laplacian differential equation with multiple deviating arguments of the form \[(\varphi_{p}(x^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-\tau_{1}(t)),\ldots,x(t-\tau_{k}(t)))+e(t).\] Some new results on the existence of periodic solutions for the previous equation are obtained.

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