Asymptotic formulas for non-oscillatory solutions of perturbed half-linear Euler equation

Pátíková, Zuzana

dc.title	Asymptotic formulas for non-oscillatory solutions of perturbed half-linear Euler equation	en
dc.contributor.author	Pátíková, Zuzana
dc.relation.ispartof	Nonlinear Analysis-Theory Methods & Applications
dc.identifier.issn	0362-546X Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2008-11-15
utb.relation.volume	69
utb.relation.issue	10
dc.citation.spage	3281
dc.citation.epage	3290
dc.type	article
dc.language.iso	en
dc.publisher	Pergamon Elsevier Science Ltd.	en
dc.identifier.doi	10.1016/j.na.2007.09.017
dc.relation.uri	https://www.sciencedirect.com/science/article/pii/S0362546X07006360
dc.subject	Half-linear differential equation	en
dc.subject	Half-linear Euler equation	en
dc.subject	Half-linear Euler-Weber equation	en
dc.subject	Modified Riccati equation	en
dc.description.abstract	We establish asymptotic formulas for non-oscillatory solutions of the half-linear second-order differential equation (Phi(x'))' + gamma/t(p) Phi(x) + c(t) Phi (x) = 0. where this equation is viewed as a perturbation of the half-linear Euler equation. (c) 2007 Elsevier Ltd. All rights reserved.	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1002128
utb.identifier.obdid	18052967
utb.identifier.scopus	2-s2.0-51349084097
utb.identifier.wok	000260237400007
utb.identifier.coden	NOAND
utb.source	j-wok
dc.date.accessioned	2011-08-16T15:06:32Z
dc.date.available	2011-08-16T15:06:32Z
utb.contributor.internalauthor	Pátíková, Zuzana
utb.fulltext.affiliation	Zuzana Patíková∗ Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic
utb.fulltext.dates	Received 13 March 2007 accepted 13 September 2007
utb.fulltext.references	[1] O. Došlý, Half-Linear Differential Equations, in: A. Cañada, P. Drábek, A. Fonda (Eds.), Handbook of Differential Equations: Ordinary Differential Equations, vol. I, Elsevier, Amsterdam, 2004, pp. 161–357. [2] O. Došlý, Perturbations of the half-linear Euler–Weber type differential equation, J. Math. Anal. Appl. 323 (2006) 426–440. [3] O. Došlý, A. Lomtatidze, Oscillation and nonoscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 36 (2006) 203–219. [4] O. Došlý, Z. Pátíková, Hille–Wintner type comparison criteria for half-linear second order differential equations, Arch. Math. 42 (2006) 185–194. [5] O. Došlý, Peňa, A linearization method in oscillation theory of half-linear differential equations, J. Inequal. Appl. 2005 (2005) 535–545. [6] O. Došlý, P. Řehák, Half-Linear Differential Equations, in: North Holland Mathematics Studies, vol. 202, Elsevier, Amsterdam, 2005. [7] O. Došlý, J. Řezníčková, Oscillation and nonoscillation of perturbed half-linear Euler differential equation, Publ. Math. Debrecen 72 (2007) 479–488. [8] O. Došlý, M. Ünal, Half-linear equations: Linearization technique and its application, J. Math. Anal. Appl. 353 (2007) 450–460. [9] A. Elbert, A. Schneider, Perturbations of the half-linear Euler differential equation, Results Math. 37 (2000) 56–83. [10] H.C. Howard, V. Maric, Regularity and nonoscillation of solutions of second order linear differential equations, Bull. T. CXIV de Acad. Serbe Sci. et Arts, Classe Sci. mat. nat. Sci. math. 20 (1990) 85–98. [11] J. Jaroš, T. Kusano, T. Tanigawa, Nonoscillation theory for second order half-linear differential equations in the framework of regular variation, Results Math. 43 (2003) 129–149. [12] J. Jaroš, T. Kusano, T. Tanigawa, Nonoscillatory half-linear differential equations and generalized Karamata functions, Nonlinear Anal. 64 (2006) 762–787. [13] V. Marić, T. Kusano, T. Tanigawa, Asymptotics of some classes of nonoscillatory solutions of second order half-linear differential equations, Bull. Cl. Sci. Math. Nat. Sci. Math. 28 (2003) 61–74. [14] Z. Pátíková, Hartman–Wintner type criteria for half-linear second order differential equations, Math. Bohem. 132 (3) (2007) 243–256. [15] J. Řezníčková, An oscillation criterion for half-linear second order differential equations, Miskolc Math. Notes 5 (2004) 203–212.
utb.fulltext.sponsorship	Research supported by the grant 201/07/0145 of the Grant Agency of the Czech Republic.
utb.fulltext.projects	GACR 201/07/0145
utb.fulltext.faculty	Faculty of Applied Informatics
utb.fulltext.ou	Department of Mathematics
utb.identifier.jel	-