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We consider a parametric double phase Dirichlet problem. In the reaction there is a superlinear perturbation term which satisfies a weak Nehari-type monotonicity condition. Using the Nehari manifold method, we show that for all parameters below a critical value, the problem has at least three nontrivial solutions all with sign information. The critical parameter value is precisely identified in terms of the spectrum of the lower exponent part of the differential operator.

We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered.

We consider a parametric Dirichlet problem driven by the (p,q)-Laplacian and a reaction which is gradient dependent (convection) and the competing effects of two more terms, one a parametric singular term and a locally defined perturbation. We show that for all small values of the parameter the problem has a positive smooth solution.

Objective: Circulating microvesicles (MV) are surrogate biomarkers of atherosclerosis. However, their role in acute coronary syndromes (ACS) has not been fully elucidated yet. We sought to examine the association of circulating apoptotic MVs with ACS pathophysiology. Approach and results: One hundred and fifty-three patients (n = 153) were included in the study; 49 patients with ST-elevation myocardial infarction (STEMI), 35 with non-STEMI (NSTEMI), 38 with unstable angina, 15 with stable coronary artery disease and 16 control individuals. Flow cytometry analysis was used to quantify circulating apoptotic/non-apoptotic (phospatidyloserine+/phospatidyloserine−) endothelial cell (EMV), red blood cell (RMV) and platelet (PMV) derived MV. Flow-mediated dilatation (FMD) of the brachial artery was assessed by ultrasound to estimate endothelial function. The inflammatory profile was assessed by serum C-reactive protein (hsCRP) levels. Apoptotic only (but not non-apoptotic) MV were increased in patients with ACS (EMV, P = 2.32 × 10−9; RMV, P = .0019; PMV, P = .01). Hierarchical clustering of the total population of ACS patients (n = 122) by circulating levels of phospatidyloserine+ EMV, RMV and PMV identified two discreet clusters of patients without any differences in traditional risk factors, but significant differences in brachial FMD (5.2% (2.5) vs. 4.1% (2.3), P < .05) that remained significant after adjustment for co-variates. The prevalence of STEMI, a surrogate for plaque rupture and vessel thrombotic occlusion, was significantly higher in the patient cluster with impaired endothelial function (60% vs 32%, P = .016, adjusted odds ratio for STEMI, 3.041, 95%CI, 1.160 to 7.968, p = .024). Conclusion: Our findings indicate that the circulating levels of apoptotic MV are increased in ACS patients and their plasma profiles associate with endothelial dysfunction and thrombotic complications in ACS patients. © 2019 Elsevier Ltd

We consider a nonlinear elliptic Dirichlet problem driven by the (p,q)-Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f(z,x) which is (p-1)-linear as x goes to + infinity. First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter lambda>0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u*_lambda and investigate the monotonicity and continuity properties of the map lambda --> u*_lambda.

We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.