Related papers: A new infinite-dimensional Linking theorem with ap…

We give a linking theorem that strengthens and unifies some many minimax theorems including Ambrosetti-Rabinowitz ``mountain pass theorem'', Rabinowitz ``multidimensional mountain pass theorem'', Rabinowitz ``saddle point theorem'' and…

A number of landmark existence theorems of nonlinear functional analysis follow in a simple and direct way from the basic separation of convex closed sets in finite dimension via elementary versions of the Knaster-Kuratowski-Mazurkiewicz…

By using the $\tau$-topology of Kryszewski and Szulkin, we establish a natural new version of the Saddle Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of a nontrivial solution of…

The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

We define a finite element method for the coupling of Stokes and nonlinear Poisson--Boltzmann equations. The novelty in the formulation is that the coupling from the electric potential to the drag in the momentum balance is rewritten as a…

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…

We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…

We study critical growth elliptic problems with jumping nonlinearities. Standard linking arguments based on decompositions of $H^1_0(\Omega)$ into eigenspaces of $- \Delta$ cannot be used to obtain nontrivial solutions to such problems. We…

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish…

We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…

We construct non-compactness examples for the fully coupled Einstein-Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional…

We employ the relative category to develop relations between the Wa\.zewski pair $(N,E)$ and the Morse decomposition of the maximal invariant set in $\ol{N\sm E}$ for infinite-dimensional dynamical systems. Via these relations, we can…

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces…

Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson…

In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…