Existence and asymptotic behavior of ground states for linearly coupled systems involving exponential growth

In this paper we study the following class of linearly coupled systems in the plane: -Delta u+u=f(1)(u)+lambda v,inR(2),-Delta v+v=f(2)(v)+lambda u,inR(2)where f(1),f(2) are continuous functions with critical exponential growth in the sense of Trudinger-Moser inequality and 0<lambda<1 is a parameter. First, for any lambda is an element of(0,1),byusing minimization arguments and minimax estimates we prove the existence of a positiveground state solution. Moreover, we study the asymptotic behavior of these solutions when lambda -> 0+. This class of systems can model phenomena in nonlinear optics and in plasma physics.