Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 101-107.

A sign-changing solution for a superlinear Dirichlet problem, II

Alfonso Castro, Pavel Drabek, & John M. Neuberger

In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of $-\Delta$ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k=1 the sign-changing exactly-once solution persists although one-sign solutions no longer exist.

Published February 28, 2003.
Subject classifications: 35J20, 35J25, 35J60.
Key words: Dirichlet problem, superlinear, subcritical, sign-changing solution, deformation lemma.

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Alfonso Castro
Division of Mathematics and Statistics
University of Texas at San Antonio
San Antonio, TX 78249-0664, USA
Pavel Drabek
Department of Mathematics
University of West Bohemia
306 14 Pilsen, Czech Republic
e-mail address:
John M. Neuberger
Department of Mathematics
Northern Arizona University
Flagstaff, AZ 86011-5717 USA
e-mail address:

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