Electronic Journal of Differential Equations,
Conference 05 (2000), pp. 1-12.
 
Title:  Explicit construction, uniqueness, and bifurcation curves 
        of solutions for a nonlinear Dirichlet problem in a ball
 
Authors: Horacio Arango (Univ. Nacional de Colombia, Medellin, Colombia)
         Jorge Cossio (Univ. Nacional de Colombia, Medellin, Colombia)
  
Abstract:
 This paper presents a method for the explicit construction of 
 radially symmetric solutions to the semilinear elliptic problem
$$\displaylines{ 
 \Delta v + f(v) = 0 \quad \hbox{in }B\cr v = 0 
 \quad \hbox{on }\partial B\,, }
$$
 where $B$ is a ball in ${\mathbb R}^N$ and $f$ is a continuous 
 piecewise linear function. Our construction method is inspired 
 on a result by E. Deumens and H. Warchall [8], and uses spline 
 of Bessel's functions. We prove uniqueness of solutions for this
 problem, with a given number of nodal regions and different 
 sign at the origin. In addition, we give a bifurcation diagram 
 when $f$ is multiplied by a parameter.

Published October 24, 2000.
Math Subject Classifications: 35B32, 35J60, 65D07, 65N99.
Key Words: Nonlinear Dirichlet problem; radially symmetric solutions; 
    bifurcation; explicit solutions; spline.