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

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*Miroslav Bartusek*

**Address.**

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

**E-mail. **bartusek@math.muni.cz

**Abstract.**

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.