The theory of metric regularity is an extension of two classical results: the Lyusternik tangent
space theorem and the Graves surjection theorem. Developments in non-smooth analysis in …

Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques
and results in many different branches of mathematics have been combined in solving …

This 2003 book presents min-max methods through a study of the different faces of the
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …

In the past, one assumed an inner-product structure to make sense of the term gradient; one
worked on a Hilbert space, or on the tangent space to a manifold, for example. However, it is …

In this paper we develop a general critical point theory to deal with existence and locations
of multiple critical points produced by minimax methods in relation to multiple invariant sets …

These lectures are devoted to a generalized critical point theory for nonsmooth functionals
and to existence of multiple solutions for quasilinear elliptic equations. If f is a continuous …

We study Brezis–Nirenberg type theorems for the equation where Ω is a bounded domain in
RN, g (x,⋅) is increasing and f is a dissipative nonlinearity. We apply such theorems for …

We apply Gamma calculus to the hypoelliptic and non-symmetric setting of Langevin
dynamics under general conditions on the potential. This extension allows us to provide …

In this article we consider shape optimization problems as optimal control problems via the
method of map**s. Instead of optimizing over a set of admissible shapes, a reference …

We discuss concepts of a regular and a critical point for a continuous function on a metric
space. Among the results presented there are: a deformation lemma providing a possibility …