5 problems

Let $z=z(t)$ denote the center position of a solitary wave in a global solution of the damped nonlinear Klein–Gordon equation with delta potential, and let $\sigma\in\{0,1\}$ and…

The nonlinear Klein–Gordon equation is considered in the setting where the linearized operator has multiple eigenvalues, and solutions with small initial data are studied under res…

Let $\phi^{0,u}$ and $\phi^{0,s}$ denote the stable and unstable solutions obtained through the Lyapunov–Perron approach, and let $C_{\mathrm{in}}$ be the constant in their leading…

Let $n$ be the spatial dimension, let $m>0$ be the Klein–Gordon mass, and let $p$ denote the power of the nonlinearity. The critical exponent under discussion is $1+\frac{2}{n}$. K…

Charged Q-balls are solitary waves of the nonlinear Klein–Gordon–Maxwell system, whose electric charge is coupled to the Maxwell field. The paper establishes their stability when t…