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Keywords:
half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria
half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria
Summary:
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 $p=2$.
References:
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