Uniqueness of positive solutions for some fourth order nonlinear equations
Résumé
In this paper we study the uniqueness question of positive solutions of the two point boundary value problem: $u^{(4)}(t)=f(u(t))$, $u(\pm R)=u'(\pm R)=0$, where $R>0$ is fixed and $f:[0,\infty)\to[0,\infty)$ is in $C^1$. A uniqueness result is proved when $f$ satisfies $00$. Some examples are also given.