Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 101--107.

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

Authors: Alfonso Castro (Univ. of Texas at San Antonio, USA)
 Pavel Drabek (Univ. of West Bohemia, Pilsen, Czech Republic)
 John M. Neuberger (Northern Arizona Univ.,Flagstaff, AZ, USA)

 
Abstract: 
 In previous  work by  Castro, Cossio, and Neuberger  \cite{ccn},
 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 {\it exactly-once} 
 solution persists although one-sign solutions no longer exist.


Published February 28, 2003.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Dirichlet problem; superlinear; subcritical; 
sign-changing solution; deformation lemma.