Applications of phase plane analysis of a Lienard system to positive solutions of Schrodinger equations

This paper deals with semilinear elliptic equations in an exterior domain of R-N with N greater than or equal to3. Sufficient conditions are obtained for the equation to have a positive solution which decays at infinity. The main result is proved by means of a supersolution-subsolution method presented by Noussair and Swanson. By using phase plane analysis of a system of Lienard type, a suitable positive supersolution is found out. Asymptotic decay estimation on a solution of the Lienard system gains a positive subsolution. Examples are given to illustrate the main result.