Periodic solutions for quasilinear complex-valued differential systems involving singular ϕ\phi-Laplacians

Topological degree is used to obtain sufficient conditions for the existence of periodic solutions of systems of second order complex- valued ordinary differential equations involving a singular $\phi$-Laplacian. Corresponding results for first order equations are also obtained

Variations on some finite-dimensional fixed-point theorems

We give rather elementary topological proofs of some generalizations of fixed-point theorems in Rⁿ due to Pireddu-Zanolin and Zgliczynski, which are useful in various questions related to ordinary differential equations.Наведено елементарнi топологiчнi доведення деяких узагальнень теорем Пiредду – Занолiна та Зглiчинського про нерухому точку в Rⁿ, якi можуть бути використанi при розглядi рiзних питань, пов’язаних iз звичайними диференцiальними рiвняннями

Nagumo conditions and second-order quasilinear equations with compatible nonlinear functional boundary conditions

We establish existence results for solutions to nonlinear functional boundary value problems for nonlinear second-order ordinary differential equations assuming there are lower and upper solutions and the right side satisfies a Nagumo growth bound. Our results contain as special cases many results for the p- and phi-Laplacians as well as many results where the boundary conditions depend on n-points or even functional

Bound sets and two-point boundary value problems for second order differential systems

summary:The solvability of second order differential systems with the classical separated or periodic boundary conditions is considered. The proofs use special classes of curvature bound sets or bound sets together with the simplest version of the Leray-Schauder continuation theorem. The special cases where the bound set is a ball, a parallelotope or a bounded convex set are considered

Blocking the receptor EP3 to PGE2 as a way to safely prevent atherothrombosis

Aspirin inhibits the platelet production of thromboxane A2 and its beneficial effect on myocardial infarction was demonstrated more than two decades ago. This result validated the strategy aimed at targeting platelet function to prevent myocardial infarction. Since then, numerous drugs targeting various activators of platelets have been developed to further improve prevention. However, the beneficial effect of all these drugs on atherothrombosis is limited by an increased risk of bleeding, because they target thrombosis effectors which are also key players in hemostasis. Since aspirin blocks the generation of numerous prostanoids, including inhibitors of platelet activation, targeting one of them might allow the antithrombotic activity to be maintained without promoting bleeding. In examining the roles of various arachidonic acid metabolites on atherothrombosis, we studied the prostaglandin E2 (PGE2). In vivo, PGE2 facilitates the responses of platelets to all their various activators through its receptor EP3. PGE2 is produced in relatively high amounts in the context of chronic inflammation such as atherosclerosis, and aggravates murine atherothrombosis. Conversely, PGE2 is not involved in hemostasis. As expected, blocking EP3 strikingly reduced atherothrombosis in mice without impacting bleeding tests. In a recent paper published in Prostaglandins & Other Lipid Mediators, we reviewed literature data about the effect of PGE2 and its receptor EP3 on platelet thrombosis and hemostasis in mice and humans. We concluded that cumulated data now justifies validating the role of EP3 blockers with phase III trials to safely improve the prevention of myocardial infarction