We prove the existence of a first nontrivial eigenvalue for an asymmetric elliptic problem with weights involving the laplacian (cf. (1.2) below) or more generally the p-laplacian (cf. (1.3) below). A first application is given to the description of the beginning of the Fučik spectrum with weights for these operators. Another application concerns the study of nonresonance for the problems (1.1) and (1.5) below. One feature of our nonresonance conditions is that they involve eigenvalues with weights instead of pointwise restrictions.  2002 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ.-Nous démontrons l'existence d'une première valeur propre non triviale pour un problème asymétrique avec poids faisant intervenir le laplacien (cf. (1.2) ci-dessous) ou plus généralement le p-laplacien (cf. (1.3) ci-dessous). Une première application consiste en la description du début du spectre de Fučik avec poids pour ces opérateurs. Une autre application concerne l'étude de la nonrésonance pour les problèmes (1.1) et (1.5) ci-dessous. Une caractéristique de nos conditions de nonrésonance est qu'elles font intervenir des valeurs propres avec poids, plutôt que des restrictions ponctuelles.  2002 Éditions scientifiques et médicales Elsevier SAS

Objective.The efficacy of antibody-based biological therapies currently used in psoriatic arthritis (PsA) depends not only on their blocking effect on the targeted molecule but also on their binding affinity to genetically defined variants of cell-surface Fc-γ receptors. Our objective was to assess the potential influence of functionally relevantFCGR2A/CD32A(H131R) andFCGR3A/CD16A(V158F) genetic polymorphisms on the EULAR response to tumor necrosis factor-α (TNF-α) blocker therapy in PsA.Methods.In total 103 patients with PsA starting anti-TNF-α therapy were included. The efficacy of therapy was evaluated according to EULAR response criteria at 3 and 6 months.FCGR2A-R131H andFCGR3A-F158V polymorphisms were genotyped. Potential correlations between clinical response and theFCGR2A-R131H andFCGR3A-F158V polymorphisms were evaluated.Results.EULAR response (moderate plus good) was 85.4% at 3 months and 87.4% at 6 months, while good EULAR response was 61.2% and 62.1%, respectively. More patients with high-affinityFCGR2Agenotypes (homozygous or heterozygous combinations) achieved a EULAR response at 6 months compared to patients with the low-affinity genotype (RR; p = 0.034, adjusted comparison error rate < 0.025). This association was due mainly to the group of patients treated with etanercept. No correlation was found for theFCGR3Apolymorphism. Similarly, no effect of C-reactive protein levels was observed.Conclusion.Our data indicate thatFCGR2Apolymorphism may influence the response to TNF-α blockers (namely etanercept) in PsA in a direction opposite to that previously found in patients with rheumatoid arthritis.

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This paper deals with the analysis of qualitative properties involved in the dynamics of Keller-Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blow-up of the solution, and the possible convergence in finite time towards a Dirac mass in terms of the three constants of the system: the mass, the flux-saturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves.1991 Mathematics Subject Classification. Primary: 35K57, 35A15, 35C07.

We prove the existence of a first nonprincipal eigenvalue for an asymmetric Neumann problem with weights involving the p-Laplacian (cf. (1.2) below). As an application we obtain a first nontrivial curve in the corresponding Fučik spectrum (cf. (1.4) below). The case where one of the weights has meanvalue zero requires some special attention in connexion with the (PS) condition and with the mountain pass geometry.