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- Sturm–Picone_comparison_theorem abstract "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 i = 1, 2, be real-valued continuous functions on the interval [a, b] and letbe two homogeneous linear second order differential equations in self-adjoint form withandLet u be a non-trivial solution of (1) with successive roots at z1 and z2 and let v be a non-trivial solution of (2). Then one of the following properties holds.There exists an x in [z1, z2] such that v(x) = 0; orthere exists a λ in R such that v(x) = λ u(x).NOTE: The first part of the conclusion is due to Sturm (1836). The second (alternative) part of this theorem is due to Picone (1910) whose simple proof was given using his now famous Picone identity. In the special case where both equations are identical one obtains the Sturm separation theorem. For an extension of this important theorem to a comparison theorem involving three or more real second order equations see the Hartman–Mingarelli comparison theorem where a simple proof was given using the Mingarelli identity.".
- Sturm–Picone_comparison_theorem wikiPageID "10162277".
- Sturm–Picone_comparison_theorem wikiPageRevisionID "551304798".
- Sturm–Picone_comparison_theorem subject Category:Ordinary_differential_equations.
- Sturm–Picone_comparison_theorem subject Category:Theorems_in_analysis.
- Sturm–Picone_comparison_theorem comment "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 i = 1, 2, be real-valued continuous functions on the interval [a, b] and letbe two homogeneous linear second order differential equations in self-adjoint form withandLet u be a non-trivial solution of (1) with successive roots at z1 and z2 and let v be a non-trivial solution of (2). ".
- Sturm–Picone_comparison_theorem label "Sturm–Picone comparison theorem".
- Sturm–Picone_comparison_theorem label "Teorema del confronto di Sturm-Picone".
- Sturm–Picone_comparison_theorem label "スツルム＝ピコーンの比較定理".
- Sturm–Picone_comparison_theorem sameAs Sturm%E2%80%93Picone_comparison_theorem.
- Sturm–Picone_comparison_theorem sameAs Teorema_del_confronto_di_Sturm-Picone.
- Sturm–Picone_comparison_theorem sameAs スツルム＝ピコーンの比較定理.
- Sturm–Picone_comparison_theorem sameAs Q3983968.
- Sturm–Picone_comparison_theorem sameAs Q3983968.
- Sturm–Picone_comparison_theorem wasDerivedFrom Sturm–Picone_comparison_theorem?oldid=551304798.