Sturm–Picone comparison theorem

Sturm–Picone comparison theorem In mathematics, in the field of ordinary differential equations, the Sturm–Picone comparison theorem, named after Jacques Charles François Sturm and Mauro Picone, is a classical theorem which provides criteria for the oscillation and non-oscillation of solutions of certain linear differential equations in the real domain.

Let pi, qi for i = 1, 2 be real-valued continuous functions on the interval [a, b] and let {displaystyle (p_{1}(x)y^{prime })^{prime }+q_{1}(x)y=0} {displaystyle (p_{2}(x)y^{prime })^{prime }+q_{2}(x)y=0} be two homogeneous linear second order differential equations in self-adjoint form with {displaystyle 0

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