an:02132828
Zbl 1103.35027
Zhang, Jihui; Li, Shujie
Multiple nontrivial solutions for some fourth-order semilinear elliptic problems
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 60, No. 2, 221-230 (2005).
00111756
2005
j
35J40 35D05 35J35 47J30 58E05
Critical group; Homological nontrivial critical point; Morse theory; Local linking; Multiple solutions; Traveling waves
The goal of the authors is to study the existence of multiple nontrivial solutions to the fourth order semilinear equation:
\[
\Delta^2u+c \Delta u=f(x,u)\text{ in }\Omega\quad u|_{\partial\Omega}=\Delta u |_{\partial\Omega}=0,\tag{1}
\]
where \(\Omega\) is a bounded open set in \(\mathbb R^N\) with smooth boundary, \(\Delta^2\) denotes the biharmonic operator, \(c\in\mathbb R\) and \(f\) is a given Carath??odory function. To this end they use Morse theory and local linking to find weak solutions.
Messoud A. Efendiev (Berlin)