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Proceedings of the American Mathematical Society

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Infinitely many radially symmetric solutions to a superlinear Dirichlet problem in a ball


Authors: Alfonso Castro and Alexandra Kurepa
Journal: Proc. Amer. Math. Soc. 101 (1987), 57-64
MSC: Primary 35J65
DOI: https://doi.org/10.1090/S0002-9939-1987-0897070-7
MathSciNet review: 897070
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0897070-7
Keywords: Superlinear Dirichlet problem, radially symmetric solution, singular ordinary differential equations, phase-plane analysis, growth condition, rapidly growing nonlinearities
Article copyright: © Copyright 1987 American Mathematical Society