Splitting subspaces and saddle points

Abstract

We prove a saddle point theorem for a functional using linking subsets of splitting subspaces. The values of the functional on one of the linking subsets do not have to be bounded away from those values on the other subset. Moreover, it does not matter which subspace is finite dimensional. Applications are given to boundary value problems for elliptic partial differential equations.

Keywords:

• elliptic partial differential equations
• saddle point methods
• Dirichlet eigenvalues

AMS:

• 35J65
• 58E05
• 49B27

¹Research supported in part by an NSF grant. 1990 Mathematics Subject Classification. Primary 35565, 58305, 49B27.

¹Research supported in part by an NSF grant. 1990 Mathematics Subject Classification. Primary 35565, 58305, 49B27.

Notes

¹Research supported in part by an NSF grant. 1990 Mathematics Subject Classification. Primary 35565, 58305, 49B27.

Additional information

Notes on contributors

Martin Schechter

1