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


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