On solutions for a class of Kirchhoff systems involving critical growth in R~2

摘要

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.