On Bounded Positive Solutions of Semilinear Schrödinger Equations

Abstract

L'equazione semilineare di Schr$\ddot{\textrm{o}}$dinger $\Delta u+f\left(x,u\right)=0$ viene considerata in un dominio esterno di $R^{n},n\geq3$. Vengono date condizioni su n sufficienti affinchè l'equazioni abbia soluzioni positive u(x) con $u\left(x\right)\rightarrow0$ quando $\mid x\mid\longrightarrow\infty$.

The semilinear Schr$\ddot{\textrm{o}}$dinger equation $\Delta u+f\left(x,u\right)=0$ is considered in an exterior domain of $R^{n},n\geq3$. Conditions on f are given which are sufficient for the equation to have positive solutions u(x) with $u\left(x\right)\rightarrow0$ as $\mid x\mid\longrightarrow\infty$.