Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order (Q1265104)

It is proved an existence and localization result for a solution of a second order semilinear elliptic problem of the type \[ Lu(x)=f(x,u(x),\nabla u(x))\quad\text{ in }\Omega,\quad u|_{\partial\Omega \setminus\Gamma}=0,\quad Bu=d\zeta \quad \text{on }\Gamma. \] The main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behavior of the right hand member of the equation. In the final section a similar result is proved for a \(p\)-Laplacian boundary value problem.