On existence of proper solutions of quasilinear second order differential equations. (English) Zbl 1115.34032

Bartušek, Miroslav; Pekárková, Eva

Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 5, 14 p. (2007).

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:

34C11	Growth and boundedness of solutions to ordinary differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations