Multiplicity results for bound state solutions of a semilinear equation

Abstract

We consider the problem of multiplicity and uniqueness of radial solutions of a nonlinear elliptic equation of the formwhere f is a prescribed function, satisfying appropriate conditions. This paper is a review of recent developments on the multiplicity of solutions, with a special emphasis on the effect of the mid-range behavior of the nonlinearity f over the existence and multiplicity of solutions.