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Zbl 1115.34032
Bartušek, Miroslav; Pekárková, Eva
On existence of proper solutions of quasilinear second order differential equations.
(English)
[J] Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 5, 14 p., electronic only (2007). ISSN 1417-3875/e

Summary: In the paper, the nonlinear differential equation $$(a(t)|y^{\prime}| ^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$$ 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.
MSC 2000:
*34C11 Qualitative theory of solutions of ODE: Growth, etc.
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

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