On existence of proper solutions of quasilinear second order differential equations
M. Bartusek, Masaryk University, Brno, Czech Republic E. J. Qualitative Theory of Diff. Equ., No. 5. (2007), pp. 1-14.
E. Pekárková, Masaryk University, Brno, Czech Republic
| Communicated by J. R. Graef. | Received on 2006-12-15 Appeared on 2007-03-12 |
Abstract: 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.
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