The mountain pass lemma of Ambrosetti and Rabinowitz is a result of great intuitive appeal as well as practical importance in the determination of critical points of functionals, particularly those which occur in he theory of ordinary and partial differential equations. In this paper we wish to point out several further results in the same direction, which are both of geometric interest and practical usefulness. Rabinowicz [Eigenvalues of nonlinear problems (Varenna, 1974), 139-195, Ed. Cremonese, Rome, 1974] posed the problem whether critical points of the kind obtained in the MPT must necessarily be saddle points. In this paper we show that under certain reasonable hypotheses the critical point must indeed be a saddle point (Theorems 6-8). Also,wes are able to derive by the same methods a number of interesting extensions of the mountain pass theorem.
Extensions of the Mountain Pass Theorem
PUCCI, Patrizia;
1984
Abstract
The mountain pass lemma of Ambrosetti and Rabinowitz is a result of great intuitive appeal as well as practical importance in the determination of critical points of functionals, particularly those which occur in he theory of ordinary and partial differential equations. In this paper we wish to point out several further results in the same direction, which are both of geometric interest and practical usefulness. Rabinowicz [Eigenvalues of nonlinear problems (Varenna, 1974), 139-195, Ed. Cremonese, Rome, 1974] posed the problem whether critical points of the kind obtained in the MPT must necessarily be saddle points. In this paper we show that under certain reasonable hypotheses the critical point must indeed be a saddle point (Theorems 6-8). Also,wes are able to derive by the same methods a number of interesting extensions of the mountain pass theorem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
