Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

• Autorzy: Jaroslav Jaroš , Kusano Takaŝi , Jelena Manojlović
• Języki publikacji: EN

Abstrakty

EN

Positive solutions of the nonlinear second-order differential equation $(p(t)|x'|^{\alpha - 1} x')' + q(t)|x|^{\beta - 1} x = 0,\alpha > \beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

Słowa kluczowe

EN

Emden-Fowler differential equations; Generalized regularly varying functions; Regularly varying solutions; Slowly varying solutions; Asymptotic behavior of solutions; Positive solutions

Kategorie tematyczne

• 34C11: Growth, boundedness
• 26A12: Rate of growth of functions, orders of infinity, slowly varying functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 12
• Strony: 2215-2233

Daty

wydano

2013-12-01

online

2013-10-08

Twórcy

autor

Jaroslav Jaroš

• Comenius University

autor

Kusano Takaŝi

• Hiroshima University

autor

Jelena Manojlović

• University of Niš

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0306-9