Castro, Alfonso; Gadam, Sudhasree

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

Electron. J. Differ. Equ. 1993(7), (1993)


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.

Mathematics Subject Classification

34B15, 35J65


lazer-mckenna conjecture, radial solutions, jumping nonlinearities