The Lazer-McKenna conjecture for radial solutions in the $\Bbb R^N$ ball

Summary

Summary: When the range of the derivative of the nonlinearity contains the first k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in [5], where the existence of k + 1 solutions was proven.

34B15, 35J65

Keywords/Phrases

lazer-mckenna conjecture, radial solutions, jumping nonlinearities