Standard reference:
$% M. Lucia, P. Macrone, and H.-S. Zhou, A Dirichlet problem with asymptotically linear and changing sign nonlinearity, Rev. Mat. Complut. 16 (2003), 465–481.%$

A Dirichlet Problem with Asymptotically Linear and Changing Sign Nonlinearity

Marcello LUCIA, Paola MACRONE,
and Huan-Song ZHOU
Dept. Math. - Hill Center
Rutgers University
110 Frelinghuysen Rd
Piscataway NJ 08854 — USA
mlucia@math.rutgers.edu
Dipartimento di Matematica
Università di Roma “Tor Vergata”
Via della Ricerca Scientifica
00133 Roma — Italy
magrone@mat.uniroma2.it
Wuhan Institute of Physics and Mathematics
Chinese Academy of Sciences
P.O. Box 71010, Wuhan 430071 — P.R. China
hszhou@wipm.ac.cn

Received: November 16, 2000
Accepted: February 27, 2003
ABSTRACT

This paper deals with the problem of finding positive solutions to the equation -Du = g(x,u) on a bounded domain _O_, with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behavior. The solutions are found using the Mountain Pass Theorem.

Key words: Elliptic equation, Asymptotically linear nonlinearity, Mountain Pass Theorem.
2000 Mathematics Subject Classification: 35J20, 35J65.