The Lazer Mckenna Conjecture for Radial Solutions in the R^N Ball

Alfonso Castro & Sudhasree Gadam

Abstract:
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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