Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 17, pp. 1-29.

Title: Some properties of Palais-Smale sequences with applications to 
       elliptic boundary-value problems 

Authors: Chao-Nien Chen (National Univ. of Education, Changhua, Taiwan)
 Shyuh-yaur Tzeng (National Univ. of Education, Changhua, Taiwan)
         
Abstract: 
When using calculus of variations to study nonlinear elliptic boundary-value
problems on unbounded domains, the Palais-Smale condition is not always
satisfied.  To overcome this difficulty, we analyze Palais-Smale sequences, and
use their convergence to justify the existence of critical points for a functional.
We show the existence of positive solutions using a minimax method and 
comparison arguments for semilinear elliptic equations.    

Submitted December 29, 1998. Published May 14, 1999.
Math Subject Classification: 35J20, 35J25.
Key Words: elliptic equation; Palais-Smale sequence; minimax method.