## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

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.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]