A mountain pass theorem (existence and bifurcation)

NOTE THE CHANGE OF TIME AND VENUE
We present a new variational characterization of multiple critical
points for even energy functionals functionals corresponding to
nonlinear Schrödinger equations of the following type:
  $
    \left\{
      \begin{array}{l}
        -\Delta u + V(x) u - q(x) |u|^\sigma u = \lambda u, \quad (x\in\mathbf{R}^N)\\
        u\in H^1(\mathbf{R}^N)\setminus\{0\}.
      \end{array}
    \right.
 $
    We assume $N\geq 3$, $q(x)\in L^\infty(\mathbf{R}^N)$, $q(x)>0$ a.e. with $\lim_{|x|\to\infty}q(x)=0$ and $0<\sigma <\frac{4}{N-2}$.
    Our results cover the following 3 cases in a uniform way:
    
    (i) $V(x)\equiv 0$;
    
(ii) $V(x)$ is a Coulomb potential and

    (iii) $V(x)\in L^\infty(\mathbf{R}^N)$ with $V(x+k)\equiv V(x)$ for all $k\in \mathbf{Z}^N$.
    
    The eigenvalue $\lambda$ thereby may or may not lie inside a spectral gap.
    Our variational characterization is ``simple'' and well suited for discussing multiple bifurcation of solutions.
http://cvgmt.sns.it/seminar/557/
            

When	Mon Nov 28, 2016 9am – 10am Coordinated Universal Time
Where	Scuola Normale Superiore, Aula Tonelli (map)