One of the existence theorems for solutions of an ordinary differential equation (cf. Differential equation, ordinary), established by G. Peano , and consisting in the following. Suppose one is given the differential equation
If the function is bounded and continuous in a region , then through each interior point of this region there passes at least one integral curve for (*). It may be that more than one integral curve passes through a certain point, e.g. for the equation there exists an infinite set of integral curves passing through :
where and are arbitrary constants.
|||G. Peano, "Démonstration de l'intégrabilité des équations différentielles ordinaires" Math. Ann. , 37 (1890) pp. 182–228|
|||I.G. Petrovskii, "Ordinary differential equations" , Prentice-Hall (1966) (Translated from Russian)|
|||P. Hartman, "Ordinary differential equations" , Birkhäuser (1982)|
Peano theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Peano_theorem&oldid=14971