Integral comparison criteria for half-linear differential equations seen as a perturbation

Pátíková, Zuzana

dc.title	Integral comparison criteria for half-linear differential equations seen as a perturbation	en
dc.contributor.author	Pátíková, Zuzana
dc.relation.ispartof	Mathematics
dc.identifier.issn	2227-7390 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2021
utb.relation.volume	9
utb.relation.issue	5
dc.citation.spage	1
dc.citation.epage	10
dc.type	article
dc.language.iso	en
dc.publisher	MDPI AG
dc.identifier.doi	10.3390/math9050502
dc.relation.uri	https://www.mdpi.com/2227-7390/9/5/502
dc.subject	half-linear differential equation	en
dc.subject	oscillation criteria	en
dc.subject	modified Riccati technique	en
dc.subject	Euler-type equation	en
dc.subject	second-order differential equation	en
dc.description.abstract	In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation). © 2021 by the authors. Licensee MDPI, Basel, Switzerland.	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1010244
utb.identifier.obdid	43882893
utb.identifier.scopus	2-s2.0-85102528899
utb.identifier.wok	000628348500001
utb.source	j-scopus
dc.date.accessioned	2021-03-23T11:20:49Z
dc.date.available	2021-03-23T11:20:49Z
dc.rights	Attribution 4.0 International
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/
dc.rights.access	openAccess
utb.ou	Department of Mathematics
utb.contributor.internalauthor	Pátíková, Zuzana
utb.fulltext.affiliation	Zuzana Pátíková https://orcid.org/0000-0003-1992-3895 Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic; patikova@utb.cz; Tel.: +420-57-603-5005
utb.fulltext.dates	Received: 1 February 2021 Accepted: 24 February 2021 Published: 1 March 2021
utb.fulltext.references	1. Došlý, O.; Pátíková, Z. Hille–Wintner-type comparison criteria for half-linear, second-order differential equations. Arch. Math. 2006, 42, 185–194. 2. Došlá, Z.; Hasil, P.; Matucci, S.; Veselý, M. Euler type linear and half-linear differential equations and their non-oscillation in the critical oscillation case. J. Inequal. Appl. 2019, 189, 1–30. http://doi.org/10.1186/s13660-019-2137-0 3. Fujimoto, K. Power comparison theorems for oscillation problems for second-order differential equations with p(t)-Laplacian. Acta Math. Hungar. 2020, 162, 333–344. http://dx.doi.org/10.1007/s10474-020-01034-5 4. Hasil, P.; Jaroš, J.; Veselý, M. Riccati technique and oscillation constant for modified euler type half-linear equations. Publ. Math. Debrecen 2020, 97, 117–147. http://dx.doi.org/10.5486/PMD.2020.8739 5. Šišoláková, J. Non-oscillation of linear and half-linear differential equations with unbounded coefficients. Math. Methods Appl. Sci. 2021, 44, 1285–1297. http://dx.doi.org/10.1002/mma.6828 6. Takaŝi, K.; Manojlović, J.V. Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions. Georgian Math. J. 2021, 28, 1–26. 7. Kusano, T.; Yosida, N. non-oscillation theorems for a class of quasilinear differential equations of second-order. Acta Math. Hungar. 1997, 76, 81–89. http://dx.doi.org/10.1007/BF02907054 8. Došlý, O.; Řehák, P. Half-Linear Differential Equations. In North Holland Mathematics Studies 202; Elsevier: Amsterdam, The Netherlands, 2005. 9. Kusano, T.; Yosida, N.; Ogata, A. Strong oscillation and non-oscillation of quasilinear differential equations of second-order. Differ. Equ. Dyn. Syst. 1994, 2, 1–10. 10. Došlý, O.; Fišnarová, S. Half-linear oscillation criteria: Perturbation in term involving derivative. Nonlinear Anal. 2010, 73, 3756–3766. http://dx.doi.org/10.1016/j.na.2010.07.049 11. Agarval, R.P.; Grace, S.R.; O’Regan, D. Oscillation Theory for Second-Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations; Kluwer Academic Publishers: Dordrecht, The Netherlands; Boston, MA, USA; London, UK, 2002. 12. Mirzov, J.D. Principal and nonprincipal solutions of a non-oscillatory system. Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 1988, 31, 100–117. 13. Fišnarová, S.; Mařík, R. Half-linear ODE and modified Riccati equation: Comparison theorems, integral characterization of principal solution. Nonlinear Anal. 2011, 74, 6427–6433. http://dx.doi.org/10.1016/j.na.2011.06.025 14. Došlý, O.; Elbert, Á. Integral characterization of the principal solution of half-linear, second-order differential equations. Studia Sci. Math. Hungar. 2000, 36, 455–469. 15. Došlý, O.; Fišnarová, S.; Mařík, R. Power comparison theorems in half-linear oscillation theory. J. Math. Anal. Appl. 2013, 401, 611–619. http://dx.doi.org/10.1016/j.jmaa.2012.12.029 16. Elbert, Á.; Schneider, A. Perturbations of the half-linear Euler differential equation. Results Math. 2000, 37, 56–83. http://dx.doi.org/10.1007/BF03322512 17. Došlý, O. Half-linear Euler differential equation and its perturbations. Electron. J. Qual. Theory Differ. Equ. 2016, 10, 1–14. 18. Fišnarová, S.; Pátíková, Z. Perturbed generalized half-linear Riemann–Weber equation - further oscillation results. Electron. J. Qual. Theory Differ. Equ. 2017, 69, 1–12. http://dx.doi.org/10.14232/ejqtde.2017.1.69 19. Hasil, P.; Veselý, M. Oscillation and non-oscillation results for solutions of perturbed half-linear equations. Math. Methods Appl. Sci. 2018, 41, 3246–3269. http://dx.doi.org/10.1002/mma.4813
utb.fulltext.sponsorship	This research received no external funding.
utb.wos.affiliation	[Patikova, Zuzana] Tomas Bata Univ Zlin, Dept Math, Stranemi 4511, Zlin 76005, Czech Republic
utb.scopus.affiliation	Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín, 760 05, Czech Republic
utb.fulltext.projects	-
utb.fulltext.faculty	Faculty of Applied Informatics
utb.fulltext.ou	Department of Mathematics
utb.identifier.jel	-