ABSTRACT
The authors examine the oscillatory behavior of solutions to a class of third order half-linear delay differential equations. The results are obtained by a comparison with first-order linear delay differential equations whose oscillatory characters are known. An example is provided to illustrate the results.
REFERENCES
[1] Agarwal, R. P.—Bohner, M.—Li, T.—Zhang, C.: Oscillation of third-order nonlinear delay differential equations, Taiwanese J. Math. 17 (2013), 545–558.10.11650/tjm.17.2013.2095Search in Google Scholar
[2] Agarwal, R. P.—Bohner, M.—Li, T.—Zhang, C.: Hille and Nehari type criteria for third-order delay dynamic equations, J. Difference Equ. Appl. 19 (2013), 1563–1579.10.1080/10236198.2013.766729Search in Google Scholar
[3] Agarwal, R. P.—Bohner, M.—Li, T.—Zhang, C.: A Philos-type theorem for third-order nonlinear retarded dynamic equations, Appl. Math. Comput. 249 (2014), 527–531.10.1016/j.amc.2014.08.109Search in Google Scholar
[4] Baculíková, B.—Dzurina, J.: Oscillation of third-order nonlinear differential equations, Appl. Math. Lett. 24 (2011), 466–470.10.1016/j.aml.2010.10.043Search in Google Scholar
[5] Bohner, M.—Grace, S. R.—Sager, I.—Tunc, E.: Oscillation of third-order nonlinear damped delay differential equations, Appl. Math. Comput. 278 (2016), 21–32.10.1016/j.amc.2015.12.036Search in Google Scholar
[6] Cecchi, M.—Marini, M.: On the oscillatory behavior of a third order nonlinear differential equation, Nonlinear Anal. 15 (1990), 141–153.10.1016/0362-546X(90)90118-ZSearch in Google Scholar
[7] Cecchi, M.—Marini, M.: Oscillation results for Emden–Fowler type differential equations, J. Math. Anal. Appl. 205 (1997), 406–422.10.1006/jmaa.1997.5206Search in Google Scholar
[8] Chatzarakis, G. E.—Dzurina, J.—Jadlovska, I.: Oscillatory and asymptotic properties of third-order quasilinear delay differential equations, J. Inequal. Appl. 2019 (2019), Article Id 23, 1–17.10.1186/s13660-019-1967-0Search in Google Scholar
[9] Grace, S. R.—Bohner, M.—Liu, A.: On Kneser solutions of third-order delay dynamic equations, Carpathian J. Math. 26 (2010), 184–192.Search in Google Scholar
[10] Grace, S. R.—Graef, J. R.—El-Beltagy, M. A.: On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (2012), 775–782.10.1016/j.camwa.2011.11.042Search in Google Scholar
[11] Grace, S. R.—Graef, J. R.—Tunc, E.: Oscillatory behavior of third order nonlinear differential equations with a nonlinear nonpositive neutral term, J. Taibah Univ. Sci. 13 (2019), 704–710.10.1080/16583655.2019.1622847Search in Google Scholar
[12] Grace, S. R.—JadlovskÁ, I.—Zafer, A.: On oscillation of third-order noncanonical delay differential equations, Appl. Math. Comput. 362 (2019), 1–7.10.1186/s13662-019-2060-1Search in Google Scholar
[13] Graef, J. R.—Saker, S. H.: Oscillation theory of third-order nonlinear functional differential equations, Hiroshima Math. J. 43 (2013), 49–72.10.32917/hmj/1368217950Search in Google Scholar
[14] Jadlovská, I.—Chatzarakis, G. E.—Dzurina, J.—Grace, S. R.: On sharp oscillation criteria for general third-order delay differential equations, Mathematics 9 (2021), 1–18.10.3390/math9141675Search in Google Scholar
[15] Koplatadze, R. G.—Chanturiya, T. A.: Oscillating and monotone solutions of first-order differential equations with deviating argument, Differ. Uravn. 18 (1982), 1463—1465 (in Russian).Search in Google Scholar
[16] Ladas, G.—Sficas, Y. G.—Stavroulakis, I. P.: Necessary and sufficient conditions for oscillations of higher order delay differential equations, Trans. Amer. Math. Soc. 285 (1984), 81–90.10.1090/S0002-9947-1984-0748831-8Search in Google Scholar
[17] Padhi, S.—Pati, S.: Theory of Third-Order Differential Equations, Springer, New Delhi, 2014.10.1007/978-81-322-1614-8Search in Google Scholar
[18] Parhi, N.—Das, P.: Asymptotic property of solutions of a class of third-order differential equations, Proc. Amer. Math. Soc. 110 (1990), 387–393.10.1090/S0002-9939-1990-1019279-4Search in Google Scholar
[19] Parhi, N.—Das, P.: Oscillation criteria for a class of nonlinear differential equations of third order, Ann. Polon. Math. 57 (1992), 219–229.10.4064/ap-57-3-219-229Search in Google Scholar
[20] Parhi, N.—Padhi, S.: On asymptotic behavior of delay-differential equations of third order, Nonlinear Anal. 34 (1998), 391–403.10.1016/S0362-546X(97)00600-7Search in Google Scholar
[21] Philos, CH. G.: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Arch. Math. (Basel) 36 (1981), 168–178.10.1007/BF01223686Search in Google Scholar
[22] Saker, S. H.—Dzurina, J.: On the oscillation of certain class of third-order nonlinear delay differential equations, Math. Bohem. 135 (2010), 225–237.10.21136/MB.2010.140700Search in Google Scholar
[23] Škerlik, A.: Integral criteria of oscillation for a third order linear differential equation, Math. Slovaca 45 (1995), 403–412.Search in Google Scholar
[24] Tunc, E.—Sahin, S.—Graef, J. R.—Pinelas, S.: New oscillation criteria for third-order differential equations with bounded and unbounded neutral coefficients, Electron. J. Qual. Theory Differ. Equ. 2021 (2021), Art. No. 46.10.14232/ejqtde.2021.1.46Search in Google Scholar
[25] Vidhyaa, K. S.—Graef, J. R.—Thandapani, E.: New oscillation results for third-order half-linear neutral differential equations, Mathematics 8 (2020), 1–9.10.3390/math8030325Search in Google Scholar
© 2023 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Parameters in Inversion Sequences
- On the Pecking Order Between Those of Mitsch and Clifford
- A Note on Cuts of Lattice-Valued Functions and Concept Lattices
- Trigonometric Sums and Riemann Zeta Function
- Notes on the Equation d(n) = d(φ(n)) and Related Inequalities
- Harmony of Asymmetric Variants of the Filbert and Lilbert Matrices in q-form
- Maximal Density and the Kappa Values for the Families {a, a + 1, 2a + 1, n} and {a, a + 1, 2a + 1, 3a + 1, n}
- Extensions in Time Scales Integral Inequalities of Jensen’s Type via Fink’s Identity
- A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions
- Extended Bromwich-Hansen Series
- Iterative Criteria for Oscillation of Third-Order Delay Differential Equations with p-Laplacian Operator
- Vallée-Poussin Theorem for Equations with Caputo Fractional Derivative
- On Oscillatory Behavior of Third Order Half-Linear Delay Differential Equations
- On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces
- Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation
- On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers
- The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions
- Type II Exponentiated Half-Logistic Gompertz-G Family of Distributions: Properties and Applications
- Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables
Articles in the same Issue
- Parameters in Inversion Sequences
- On the Pecking Order Between Those of Mitsch and Clifford
- A Note on Cuts of Lattice-Valued Functions and Concept Lattices
- Trigonometric Sums and Riemann Zeta Function
- Notes on the Equation d(n) = d(φ(n)) and Related Inequalities
- Harmony of Asymmetric Variants of the Filbert and Lilbert Matrices in q-form
- Maximal Density and the Kappa Values for the Families {a, a + 1, 2a + 1, n} and {a, a + 1, 2a + 1, 3a + 1, n}
- Extensions in Time Scales Integral Inequalities of Jensen’s Type via Fink’s Identity
- A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions
- Extended Bromwich-Hansen Series
- Iterative Criteria for Oscillation of Third-Order Delay Differential Equations with p-Laplacian Operator
- Vallée-Poussin Theorem for Equations with Caputo Fractional Derivative
- On Oscillatory Behavior of Third Order Half-Linear Delay Differential Equations
- On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces
- Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation
- On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers
- The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions
- Type II Exponentiated Half-Logistic Gompertz-G Family of Distributions: Properties and Applications
- Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables