Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations

Author:

Hassan Taher S.123ORCID,Iambor Loredana Florentina4ORCID,Mureşan Sorin4,Alenzi Khalid1,Odinaev Ismoil5ORCID,Rashedi Khudhayr A.1

Affiliation:

1. Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

3. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

4. Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania

5. Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia

Abstract

This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results.

Funder

Scientific Research Deanship at University of Ha’il, Saudi Arabia

Publisher

MDPI AG

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