A remark on global smooth solutions for quasilinear wave equations
Using a perturbation argument based on a finite dimensional reduction, we find positive solutions to a given class of perturbed degenerate elliptic equations with critical growth.
We prove a formula relating the index of a solution and the rotation number of a certain complex vector along bifurcation diagrams.
We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain under the general outflow condition. Let be a 2-dimensional straight channel . We suppose that is bounded and that . Let be a Poiseuille flow in and the flux of . We look for a solution which tends to as . Assuming that the domain and the boundary data are symmetric with respect to the -axis, and that the axis intersects every component of the boundary, we have shown the existence...