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Reference.org
Sturm separation theorem
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, in the field of <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">ordinary differential equations</a>, Sturm separation theorem, named after <a href="/facts/Jacques_Charles_Fran%C3%A7ois_Sturm/N9F0StnF">Jacques Charles François Sturm</a>, describes the location of roots of solutions of <a href="/facts/Homogeneous_differential_equation/UmTJCNEh">homogeneous</a> <a href="/facts/Order_(differential_equation)/9MGbE3Ca">second order</a> <a href="/facts/Linear_differential_equation/nLEbIIVf">linear differential equations</a>. Basically the theorem states that given two linear independent solutions of such an equation the zeros of the two solutions are alternating. </p>