## 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

CPAA

We study the dynamics for the focusing nonlinear Klein Gordon equation with a positive, singular, radial potential and initial data in energy space. More precisely, we deal with

$u_{tt}-Δ u+m^2 u=|x|^{-a}|u|^{p-1}u$ |

with

. In dimension

, we establish the existence and uniqueness of the ground state solution that enables us to define a threshold size for the initial data that separates global existence and blow-up. We find a critical exponent depending on

. We establish a global existence result for subcritical exponents and subcritical energy data. For subcritical exponents and critical energy some solutions blow-up, other solutions exist for all time due to the decomposition of the energy space of the initial data into two complementary sets.

$0 < a < 2$ |

$d≥3$ |

$a$ |

DCDS

We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

DCDS

We prove that every one-dimensional real Ambrosio-Kirchheim current with
zero boundary (i.e. a cycle) in a lot of reasonable spaces (including all finite-dimensional normed spaces)
can be represented by a Lipschitz curve parameterized over the real line through a suitable limit
of Cesàro means of this curve over a subsequence of symmetric bounded intervals (viewed as currents). It is further shown that in such spaces,
if a
cycle is indecomposable, i.e. does not contain ``nontrivial'' subcycles, then it can be represented
again by a Lipschitz curve parameterized over the real line through a limit
of Cesàro means of this curve over every sequence of symmetric bounded intervals, that is, in other words, such a cycle
is a solenoid.

keywords:
Ambrosio-Kirchheim currents
,
solenoids.
,
metric currents
,
Lipschitz curves
,
Normal currents

DCDS

The work treats smoothing and dispersive
properties of solutions to the Schrödinger equation with
magnetic potential. Under suitable smallness assumption on the
potential involving scale invariant norms we prove smoothing -
Strichartz estimate for the corresponding Cauchy problem. An
application that guarantees absence of pure point spectrum of the
corresponding perturbed Laplace operator is discussed too.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]