Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 21-31.

Existence of many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli

Alfonso Castro & Marcel B. Finan

We study the existence of many positive nonradial solutions of a superlinear Dirichlet problem in an annulus in RN. 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 sign-changing 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
Marcel B. Finan
Department of Mathematics
The University of Texas at Austin
Austin, TX 78712 USA.

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