The intrinsic mountain pass

Martin Schechter

Vol. 171 (1995), No. 2, 529–544

DOI: 10.2140/pjm.1995.171.529

Abstract

We show how the mountain pass and saddle point theorems can be formulated with out the use of “auxiliary” sets. Moreover, we show that results can still be obtained when some basic hypotheses of these theorems are not satisfied. We then apply our results to semilinear problems for partial differential equations.

Mathematical Subject Classification 2000

Primary: 58E05

Secondary: 35J65, 47H15

Milestones

Received: 5 April 1993

Revised: 19 January 1994

Published: 1 December 1995