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
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 |
This paper deals with the problem of finding positive solutions to the equation -u = g(x,u) on a bounded domain , 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.