On solutions for a class of Kirchhoff systems involving critical growth in R2

In this work we study the existence of solutions for the following class of elliptic systems involving Kirchhoff equations in the plane: {m(parallel to u parallel to(2))[-Delta u + u] =lambda f(u, v), x is an element of R-2, l parallel to v parallel to(2))[-Delta v + v] = lambda g(u, v), x is an element of R-2, where lambda > 0 is a parameter, m, l : [0,+infinity) -> [0,+infinity) are Kirchhoff-type functions, parallel to center dot parallel to denotes the usual norm of the Sobolev space H1(R2) and the nonlinear terms f and g have exponential critical growth of Trudinger-Moser type. Moreover, when f and g are odd functions, we prove that the number of solutions increases when the parameter lambda becomes large.