arXiv subjects

Fabrice Colin

Publications and source records attributed to Fabrice Colin.

8 recordsLinked to original sources

arXiv2026

Linking theorems for multivalued functionals and application to partial differential inclusions

Using the framework of critical point theory for multivalued functionals developed in \cite{Fri}, we establish some linking theorems for such functionals, which generalizes \cite[Theorem 2.11]{Wi}, \cite[Theorem 2.12]{Wi} and \cite[Theorem 2.12]{Fri}. The proofs of our abstract results rely on a general minimax principle for multivalued mappings. As an application, we obtain a nontrivial solution of a semilinear Dirichlet boundary value problem for partial differential inclusions.

math.AP↗

arXiv2025

An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems

The purpose of this paper is to establish a critical point theorem, which is an infinite-dimensional generalization of the classical generalized Mountain Pass Theorem of P. H. Rabinowitz \cite[Theorem 5.3]{Ra}. As application, we obtain the existence of at least one solution to a semilinear elliptic systems with indefinite weights in $\mathbb{R}^2$.

math.AP↗

arXiv2025

On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$

In this work, we establish a continuous version of the Fountain theorem by using the framework of the weak slope for continuous functionals, which generalizes Theorem 3.6 of Willem \cite{Wi}. Then we present an application to a semilinear problem.

math.AP↗

arXiv2025

A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $\tau-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations.

math.AP↗

arXiv2025

An infinite dimensional saddle point theorem and application

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 strongly indefinite semilinear Schr\"odinger equation where the associated functional is indefinite, that is, the functional is of the form $J(u) = \dfrac{1}{2} \langle Lu, u \rangle - \Psi(u)$ defined on a Hilbert space $X$, where $L : X \to X$ is a self-adjoint operator with negative and positive eigenspace both infinite-dimensional.

math.AP↗

arXiv2018

An Orbitrap-based laser desorption/ablation mass spectrometer designed for spaceflight

RATIONALE: The investigation of cryogenic planetary environments as potential harbors for extant life and/or contemporary sites of organic synthesis represents an emerging focal point in planetary exploration. Next generation instruments need to be capable of unambiguously determining elemental and/or molecular stoichiometry via highly accurate mass measurements and the separation of isobaric interferences. METHODS: An OrbitrapTM analyzer adapted for spaceflight (referred to as the CosmOrbitrap), coupled with a commercial pulsed UV laser source (266 nm), is shown to successfully characterize a variety of planetary analog samples via ultrahigh resolution laser desorption/ablation mass spectrometry. The materials analyzed in this study include: jarosite (a hydrous sulfate detected on Mars); magnesium sulfate (a potential component of the subsurface ocean on Europa); uracil (a nucleobase of RNA); and a variety of amino acids. RESULTS: The instrument configuration tested here enables: measurement of major elements and organic molecules with ultrahigh mass resolution (m/Δm higher than 120,000, FWHM); quantification of isotopic abundances with 1.0% (2σ) precision; and, identification of highly accurate masses within 3.2 ppm of absolute values. The analysis of a residue of a dilute solution of amino acids demonstrates the capacity to detect twelve amino acids in positive ion mode at concentrations as low as 1 pmol/mm2 while maintaining mass resolution and accuracy requirements. CONCLUSIONS: The CosmOrbitrap mass analyzer is highly sensitive and delivers mass resolution/accuracy unmatched by any instrument sent into orbit or launched into deep space. This prototype instrument, which maps to a spaceflight implementation, represents a missionenabling technology capable of advancing planetary exploration for decades to come.

astro-ph.EP↗

arXiv2014

On differential systems with strongly indefinite variational structure

We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the effect that the nonlinear terms have to satisfy the Ambrosetti-Rabinowitz superquadratic condition. To establish the existence of solutions, a new version of the symmetric mountain pass theorem for strongly indefinite functionals is presented in this paper. This theorem is subsequently applied to deal with cases where all the Palais-Smale sequences of the energy functional may be unbounded.

math.AP↗

arXiv2013

Generalized fountain theorem and application to strongly indefinite semilinear problems

By using the degree theory and the $τ-$topology of Kryszewski and Szulkin, we establish a version of the Fountain Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of infinitely many solutions of two strongly indefinite semilinear problems including the semilinear Schrödinger equation.

math.AP↗