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Article

New Theorems for Oscillations to Differential Equations with Mixed Delays

1
Department of Mathematics, JIS College of Engineering, Kalyani 741235, India
2
Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
3
Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
4
Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia
5
Department of Mathematics and Computers Science, Transilvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Youssef N. Raffoul
Symmetry 2021, 13(3), 367; https://doi.org/10.3390/sym13030367
Received: 8 February 2021 / Revised: 19 February 2021 / Accepted: 23 February 2021 / Published: 25 February 2021
The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p(ι)w(ι)α+r(ι)uβ(ν(ι))=0,ιι0 where w(ι)=u(ι)+q(ι)u(ζ(ι)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples. View Full-Text
Keywords: Lebesgue’s dominated convergence theorem; neutral; oscillation; nonoscillation; non-linear Lebesgue’s dominated convergence theorem; neutral; oscillation; nonoscillation; non-linear
MDPI and ACS Style

Santra, S.S.; Majumder, D.; Bhattacharjee, R.; Bazighifan, O.; Khedher, K.M.; Marin, M. New Theorems for Oscillations to Differential Equations with Mixed Delays. Symmetry 2021, 13, 367. https://doi.org/10.3390/sym13030367

AMA Style

Santra SS, Majumder D, Bhattacharjee R, Bazighifan O, Khedher KM, Marin M. New Theorems for Oscillations to Differential Equations with Mixed Delays. Symmetry. 2021; 13(3):367. https://doi.org/10.3390/sym13030367

Chicago/Turabian Style

Santra, Shyam S., Debasish Majumder, Rupak Bhattacharjee, Omar Bazighifan, Khaled M. Khedher, and Marin Marin. 2021. "New Theorems for Oscillations to Differential Equations with Mixed Delays" Symmetry 13, no. 3: 367. https://doi.org/10.3390/sym13030367

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