Electron.n. J. Diff. Eqns. Vol. 1993(1993), No. 07, pp. 1-6.

The Lazer Mckenna Conjecture for Radial Solutions in the RN Ball

Alfonso Castro & Sudhasree Gadam

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.

Submitted May 2, 1993. Published October 30, 1993.
Math Subject Classification: 34B15, 35J65.
Key Words: Lazer-McKenna conjecture, radial solutions, jumping nonlinearities.

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Alfonso Castro
Department of Mathematics, University of Texas
San Antonio, TX 78249, USA
E-mail: acastro@utsa.edu
Sudhasree Gadam
Department of Mathematics, University of North Texas
Denton, TX 76203, USA

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