Energy estimated frequencies of standing-wave solutions to non-linear Klein-Gordon systems in higher dimension

2010/05/02 by Garrisi, Daniele
#35A15 #35J50 #37K40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1005.0134

Abstract

In this work a system of non-linear elliptic equations is considered, where the non-linear term is the sum of a quadratic form and a Sobolev sub-critical term. An extra assumption is introduced on the sub-critical term, which is minimal among the ones which guarantee the existence of standing-waves obtained by estimating frequencies of minimizing sequences with the energy functional.

Related

• Multiple normalized standing-waves solutions to the scalar non-linear\n Klein-Gordon equation with two competing powers
• Stability and instability of standing-wave solutions to one dimensional quadratic-cubic Klein-Gordon equations
• On the orbital stability of standing-waves solutions to a coupled non-linear Klein-Gordon equation
• Finite energy standing waves for the Klein-Gordon-Maxwell system: the limit case
• Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension