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.
© 1987 American Mathematical Society
Castro, Alfonso and Kurepa, Alexandra, "Infinitely Many Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball" (1987). All HMC Faculty Publications and Research. 460.
First published in Proceedings of the American Mathematical Society in Vol 101-1(1987), published by the American Mathematical Society