Sturm-Picone comparison theorem
= Sturm-Picone comparison theorem
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{wiki=Sturm–Picone_comparison_theorem}
For two real self-adjoint equations $(p_i y_i\prime)\prime+q_i y_i=0$ with continuous coefficients, $0<p_2\leq p_1$ and $q_1\leq q_2$, between consecutive zeros of a nontrivial first solution a nontrivial second solution either has a zero or is proportional to the first there. This comparison controls oscillation through the coefficients.