Global Existence for Quasilinear Dispersive Equations Ii

Global Existence for Quasilinear Dispersive Equations

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Quasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

Quasilinear Schrödinger Equations I: Small Data and Quadratic Interactions

In this article we prove local well-posedness in lowregularity Sobolev spaces for general quasilinear Schrödinger equations. These results represent improvements of the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence of solutions in very high regularity spaces. Our arguments here are purely dispersive. The function spaces i...

Almost Global Existence for Quasilinear Wave Equations in Three Space Dimensions

This article studies almost global existence for solutions of quadratically quasilinear systems of wave equations in three space dimensions. The approach here uses only the classical invariance of the wave operator under translations, spatial rotations, and scaling. Using these techniques we can handle wave equations in Minkowski space or Dirichletwave equations in the exterior of a smooth, sta...