Nonradial solutions of weighted elliptic superlinear problems in bounded symmetric domains

2020/03/27 by Hugo Aduén, Aduén, Hugo, Sigifredo Herrón +1
Mathematics · #35A02 #35A24 #35J60 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A02 #msc:35A24 #msc:35J60 #msc:35J61

paper · pdf · doi:10.48550/arxiv.2003.12617

8 pages, it is a research

arxiv created 2020/03/27 · arxiv updated 2020/03/31

Abstract

The present work has two objectives. First, we prove that a weight\-ed superlinear elliptic problem has infinitely many nonradial solutions in the unit ball. Second, we obtain the same conclusion in annuli for a more general nonlinearity which also involves a weight. We use a lower estimate of the energy level of radial solutions with k-1 zeros in the interior of the domain and a simple counting. Uniqueness results due to Tanaka \cite[2008]Tanaka1 and \cite[2007]Tanaka2 are very useful in our approach.

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