Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 2131.
Existence of many positive nonradial solutions for a
superlinear Dirichlet problem on thin annuli
Alfonso Castro & Marcel B. Finan
Abstract:
We study the existence of many positive nonradial solutions of a
superlinear Dirichlet problem in an annulus in R^{N}. Our
strategy consists of finding the minimizer of the energy
functional restricted to the Nehrai manifold of a subspace of
functions with symmetries. The minimizer is a global critical point
and therefore is a desired solution. Then we show that the minimal
energy solutions in different symmetric classes have mutually
different energies. The same approach has been used to prove the
existence of many signchanging nonradial solutions (see [5[).
Published October 24, 2000.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Superlinear Dirichlet problem, positive nonradial
solutions, variational methods.
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Alfonso Castro
Department of Mathematics,
University of Texas
San Antonio, TX 78249, USA
email: castro@math.utsa.edu 

Marcel B. Finan
Department of Mathematics
The University of Texas at Austin
Austin, TX 78712 USA.
email: mbfinan@math.utexas.edu

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