Applications of phase plane analysis of a Liénard system to positive solutions of Schrödinger equations

Jitsuro Sugie, Naoto Yamaoka
2002 Proceedings of the American Mathematical Society  
This paper deals with semilinear elliptic equations in an exterior domain of R N with N ≥ 3. 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 Liénard type, a suitable positive supersolution is found out. Asymptotic decay estimation on a solution of the Liénard system gains a positive
more » ... ins a positive subsolution. Examples are given to illustrate the main result.
doi:10.1090/s0002-9939-02-06681-9 fatcat:csylox4jxzeljfnabyxnvj5aki