### Multiple solutions for a null mass Neumann problem in exterior domains

#### Abstract

In this paper we study the existence and multiplicity of solutions for the semilinear elliptic equation $-\Delta u = Q(x)f'(u)$ in an exterior domain with Neumann boundary conditions. We prove the existence of a positive ground state as well as a sign-changing solution under a double power growth condition on the nonlinearity.

#### Article information

Source
Adv. Differential Equations Volume 15, Number 1/2 (2010), 181-199.

Dates
First available in Project Euclid: 18 December 2012