Singular solutions for the differential equation with $p$-Laplacian

Miroslav Bartusek

Faculty of Sciences, Masaryk University, Department of Mathematics, Janackovo nam. 2a, 662 95 Brno, Czech Republic


In the paper a sufficient condition for all solutions of the differential equation with $p$-Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations $(|y'|^{p-1} y')' + r(t) |y|^\lambda \sgn y = 0$, $r>0$ are given for which singular solutions exist (for any $p>0$, $\lambda > 0$, $p\neq \lambda$).

AMSclassification. 34C10, 34C15, 34D05.

Keywords. Singular solutions, noncontinuable solutions, second order equations.