Electron. J. Diff. Eqns., Vol. 2008(2008), No. 122, pp. 1-13.

A global approach to ground state solutions

Philip Korman

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.

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Philip Korman
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, OH 45221-0025, USA
email: kormanp@math.uc.edu

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