Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 112.
Explicit construction, uniqueness, and bifurcation curves
of solutions for a nonlinear Dirichlet problem in a ball
Horacio Arango & Jorge Cossio
Abstract:
This paper presents a method for the explicit construction of
radially symmetric solutions to the semilinear elliptic problem
where
is a ball in
and
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
is
multiplied by a parameter.
Published Ocotber 24, 2000.
Math Subject Classifications: 35B32, 35J60, 65D07, 65N99.
Key Words: Nonlinear Dirichlet problem, radially symmetric solutions,
bifurcation, explicit solutions, spline.
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Horacio Arango
Departamento de Matematicas
Universidad Nacional de Colombia
Apartado Aereo 3840
Medellin, Colombia 

Jorge Cossio
Departamento de Matematicas
Universidad Nacional de Colombia
Apartado Aereo 3840
Medellin, Colombia
email: jcossio@perseus.unalmed.edu.co 
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