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PROC

We study a class of quasilinear elliptic equations suggested by C.H. Derrick
in 1964 as models for elementary particles. For scalar fields we prove some new
nonexistence results. For vector-valued fields the situation is different as shown by
recent results concerning the existence of solitary waves with a topological constraint.

DCDS

This paper is concerned with the Klein-Gordon-Maxwell system in a bounded space domain. We
discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in
equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We
assume homogeneous Dirichlet boundary conditions on $u$ and non homogeneous
Neumann boundary conditions on $\phi$. In the "linear" case we prove the existence of a nontrivial
solution when the coupling constant is sufficiently small. Moreover we show that a suitable nonlinear perturbation in
the matter equation gives rise to infinitely many solutions.
These problems have a variational structure so that we can apply
global variational methods.

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