##
Conjugacy criteria for half-linear differential equations

##
*
Simon Pena
*

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

** E-mail:**

**Abstract.**
Sufficient conditions on the function $c(t)$ ensuring that the
half-linear second order differential equation
$$
(|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2}
u(t)=0\,, \quad \quad p>1
$$
possesses a nontrivial solution having at least two zeros in a
given interval are obtained. These conditions extend some
recently proved conjugacy criteria for linear equations which
correspond to the case $p=2$.

**AMSclassification.**
34C10

**Keywords.**
Half-linear equation, scalar $p$-Laplacian, conjugate
points, conjugacy criteria