Global Solutions for a Semilinear 2d Klein-gordon Equation with Exponential Type Nonlinearity

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity

On a bounded smooth domain Ω ⊂ R we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to ∂Ω. We derive global a priori bounds of the Keller–Osserman type. Using a Phragmen–Lindelöf alternative for generalized sub and super-harmonic functions we discuss existence, nonexistence and uniqueness of so-called large solut...

Global existence in infinite lattices of nonlinear oscillators: The Discrete Klein-Gordon equation

Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice-we prove either global existence or nonexistence in time, for the Discrete Klein-Gordon equation with the same type...

Analyticity of the Scattering Operator for Semilinear Dispersive Equations

We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of the Schrödinger equation with powerlike nonlinearity or with Hartree type nonlinearity, and in the case of the wave and Klein–Gordon equations with power nonl...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION