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Uniqueness of large radial solutions and existence of nonradial solutions for a superlinear Dirichlet problem in annulii |
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| Authors: | Hugo Adué n |
| Affiliation: | a Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería, Colombia b Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA c Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia |
| Abstract: | Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k>0 large, there exist exactly two radial solutions with k nodal regions (connected components of  ). The problem need not be homogeneous. |
| Keywords: | Critical point Morse index Nonradial solutions Cwikel inequality Nonlinear elliptic equation |
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