Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 122, pp. 1-13.

Title: A global approach to ground state solutions
  
Author: Philip Korman (Univ. of Cincinnati, Cincinnati, Ohio, USA)
 
Abstract:
 We study radial solutions of semilinear Laplace equations.
 We try to understand all solutions of the problem, regardless
 of the boundary behavior. It turns out that one can study
 uniqueness or multiplicity properties of ground state solutions
 by considering curves of solutions of the corresponding Dirichlet
 and Neumann problems. We show that uniqueness of ground state
 solutions can  sometimes  be approached by a numerical computation.
 
Submitted March 24, 2008. Published August 28, 2008.
Math Subject Classifications: 35J60, 65N25.
Key Words: Solution curves; ground state solutions.