On existence of proper solutions of quasilinear second order differential equations | Zendy

Miroslav Bartušek | Zendy; Eva Pekárková | Zendy

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On existence of proper solutions of quasilinear second order differential equations

Author(s) -

Miroslav Bartušek,

Eva Pekárková

Publication year - 2007

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2007.1.5

Subject(s) - mathematics , order (exchange) , differential equation , mathematical analysis , differential (mechanical device) , calculus (dental) , thermodynamics , economics , physics , medicine , finance , dentistry

In the paper, the nonlinear differential equation (a(t)|y 0 | p 1 y 0 ) 0 + b(t)g(y 0 ) + r(t)f(y) = e(t) is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutions to be proper are derived. Sufficient conditions for the nonexistence of weakly oscillatory solutions are given.

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