Standard reference:
$% M. Lucia, P. Macrone, and H.-S. Zhou, A Dirichlet problem with asymptotically linear and changing sign nonlinearity, Rev. Mat. Complut. 16 (2003), 465481.%$

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
Dipartimento di Matematica
Università di Roma “Tor Vergata”
Via della Ricerca Scientifica
00133 Roma Italy
Wuhan Institute of Physics and Mathematics
Chinese Academy of Sciences
P.O. Box 71010, Wuhan 430071 P.R. China

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.