The Dirichlet problem for quasimonotone systems of second order equations (Q1880976)

Let \(E\) be a finite-dimensional real vector space ordered by a solid cone. Consider the Dirichlet boundary value problem \[ u''(t)=f\bigl(t,u(t) \bigr),\;t\in[0,1],\;u(0)=u(1)=0,\tag{D} \] where \(f:[0,1]\times E\to E\) is continuous and quasimonotone in \(u\) for \(t\in[0,1]\). Using the method of lower and upper solutions, the author proves the existence of a solution \(u\in C^2([0,1],E)\) of (D).