Three nontrivial solutions for noncoercive asymptotically linear elliptic problems
In this paper we consider a semilinear elliptic equation. We assume that the right and side nonlinearity is asymptotically linear and our conditions on it imply that the Euler functional of the problem is noncoercive. Using variational methods coupled with Morse theory and in particular the use of critical groups, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. © 2011 University of Houston.
Critical point of mountain pass-type, Local minimizer, PS-condition
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Three nontrivial solutions for noncoercive asymptotically linear elliptic problems." Houston journal of mathematics 37, no. 2 (2011): 559-576.
Houston Journal of Mathematics