Theorem of Scorza Dragoni

In calculus , Scorza Dragoni's theorem says :

The real boundary value problem

${\displaystyle u''(x)=f(x,u(x),u'(x)),\quad u(a)=u(b)=0}$

is solvable if is continuous and bounded . ${\displaystyle f\colon [a,b]\times \mathbb {R} ^{2}\to \mathbb {R} }$

The sentence does not provide a statement about the uniqueness of the solution. The proof of the theorem can be done with Schauder's fixed point theorem .

The theorem was proved in 1935 by the Italian mathematician Giuseppe Scorza Dragoni .

literature

• Etienne Emmrich: Ordinary and Operator Differential Equations . Vieweg Friedr. + Sohn Ver, ISBN 9783528032135 .