Radial strong solutions to a coupled system of nonlinear Euclidean bosonic equations

This paper is concerned with nontrivial radial strong solutions to a class of coupled nonlinear Euclidean bosonic equations, which arise from the string theory and cosmology. First, we establish a variational framework to study the coupled system and prove the existence of nontrivial radial strong solutions. Furthermore, we investigate the asymptotic behavior of these radial strong solutions. By using monotonicity method, we prove that as the coupling coefficient goes to zero, these radial solutions converge to a radial strong solution of the corresponding uncoupled problem.