# Tagged Questions

Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

700 views

### Nonlinear PDE and Green functions

This is somewhat of a curiosity that can hide somewhat deeper. For a Green function of a nonlinear PDE I mean something like $$\partial^2\phi+V(\phi)=\delta^D(x).$$ I do not know if a real ...
124 views

203 views

### Convergence rate of iterated nonlinear equations?

For $i=1, \dots, n$ ($n$ could be large) we have variables $x_i$ and $y_i$ relating to probability bounds s.t. $x_i, y_i \geq 0, x_i+y_i \leq 1 \; \forall i$. Each $i$ has a constant $\theta_i$, and ...
75 views

163 views

### Integrability of ground state solution for elliptic equation

For the solution of semi-linear elliptic equation, for example I'm considering the 2D cubic nonlinear Schroedinger equation, the correspongding elliptic equation is $\Delta u+u^3=u$, with $u>0$. By ...
332 views

### Variational Formulation of Boundary Value Problems With Unknown on the boundary

Suppose that we have a linear operator equation on $\Omega$ with Lipschitz boundary $\partial \Omega$, \begin{eqnarray} Lu &=& \frac{\partial u}{\partial t}, u(x,0) &=& u_0 \; \; \...