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.scopus.affiliation	Pátíková Z., Department of Mathematics, Tomas Bata University in Zlín, 760 05 Zlín, Nad Stráněmi 4511, 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	-