Infinitely Many Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball
Open Access
- 1 September 1987
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 101 (1), 57-64
- https://doi.org/10.2307/2046550
Abstract
In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions for the associated singular ordinary differential equation.Keywords
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