Search results for "UNIQUE"
showing 10 items of 268 documents
A singularly perturbed Kirchhoff problem revisited
2020
Abstract In this paper, we revisit the singularly perturbation problem (0.1) − ( ϵ 2 a + ϵ b ∫ R 3 | ∇ u | 2 ) Δ u + V ( x ) u = | u | p − 1 u in R 3 , where a , b , ϵ > 0 , 1 p 5 are constants and V is a potential function. First we establish the uniqueness and nondegeneracy of positive solutions to the limiting Kirchhoff problem − ( a + b ∫ R 3 | ∇ u | 2 ) Δ u + u = | u | p − 1 u in R 3 . Then, combining this nondegeneracy result and Lyapunov-Schmidt reduction method, we derive the existence of solutions to (0.1) for ϵ > 0 sufficiently small. Finally, we establish a local uniqueness result for such derived solutions using this nondegeneracy result and a type of local Pohozaev identity.
Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient ter…
2011
Abstract In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum: where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator, sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.
L∞-variational problems associated to measurable Finsler structures
2016
Abstract We study L ∞ -variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.
Inverse problems for $p$-Laplace type equations under monotonicity assumptions
2016
We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for $p$-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.
The Uniqueness of Planktonic Ecosystems in the Mediterranean Sea: The Response to Orbital- and Suborbital-Climatic Forcing over the Last 130,000 Years
2016
AbstractThe Mediterranean Sea is an ideal location to test the response of organisms to hydrological transformations driven by climate change. Here we review studies carried out on planktonic foraminifera and coccolithophores during the late Quaternary and attempt the comparison of data scattered in time and space. We highlight the prompt response of surface water ecosystems to both orbital- and suborbital-climatic variations.A markedly different spatial response was observed in calcareous plankton assemblages, possibly due to the influence of the North Atlantic climatic system in the western, central and northern areas and of the monsoon system in the easternmost and southern sites. Orbita…
La faune ammonitique des marnes à fossiles ferrugineux de la région de Niort, France (Oxfordien inférieur, Zone à Cordatum, Sous-Zone à Cordatum)
2009
21 pages; Une nouvelle récolte d'ammonites dans les marnes à ammonites ferrugineuses de la région de Niort (France), autrefois étudiées par de GROSSOUVRE (1922), apporte de très nombreuses informations biostratigraphiques, paléoenvironnementales et paléobiogéographiques. La faune est datée de l'Oxfordien inférieur : Zone à Cordatum, Sous-Zone à Cordatum, partie inférieure probable. De plus, elle est unique en Europe occidentale 1) par les espèces trouvées -dont certaines ne semblent connues que dans ce gisement- 2) par la domination très atypique du binôme Taramelliceras - Creniceras qui représente les 2/3 des individus. Enfin, le spectre faunique plaide en faveur d'un milieu de plate-forme…
Distinct lytic vacuolar compartments are embedded inside the protein storage vacuole of dry and germinating Arabidopsis thaliana seeds.
2011
International audience; Plant cell vacuoles are diverse and dynamic structures. In particular, during seed germination, the protein storage vacuoles are rapidly replaced by a central lytic vacuole enabling rapid elongation of embryo cells. In this study, we investigate the dynamic remodeling of vacuolar compartments during Arabidopsis seed germination using immunocytochemistry with antibodies against tonoplast intrinsic protein (TIP) isoforms as well as proteins involved in nutrient mobilization and vacuolar acidification. Our results confirm the existence of a lytic compartment embedded in the protein storage vacuole of dry seeds, decorated by γ-TIP, the vacuolar proton pumping pyrophospha…
Sliding solutions of second-order differential equations with discontinuous right-hand side
2017
We consider second-order ordinary differential equations with discontinuous right-hand side. We analyze the concept of solution of this kind of equations and determine analytical conditions that are satisfied by typical solutions. Moreover, the existence and uniqueness of solutions and sliding solutions are studied. Copyright © 2017 John Wiley & Sons, Ltd.
A singular elliptic equation and a related functional
2021
We study a class of Dirichlet boundary value problems whose prototype is [see formula in PDF] where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on [see formula in PDF] whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Molecular basis of SARS-CoV-2 infection and rational design of potential antiviral agents: Modeling and simulation approaches
2020
International audience; The emergence in late 2019 of the coronavirus SARS-CoV-2 has resulted in the breakthrough of the COVID-19 pandemic that is presently affecting a growing number of countries. The development of the pandemic has also prompted an unprecedented effort of the scientific community to understand the molecular bases of the virus infection and to propose rational drug design strategies able to alleviate the serious COVID-19 morbidity. In this context, a strong synergy between the structural biophysics and molecular modeling and simulation communities has emerged, resolving at the atomistic level the crucial protein apparatus of the virus and revealing the dynamic aspects of k…