NORMALIZED GROUND STATE SOLUTIONS FOR KIRCHHOFF EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2

We are concerned with normalized solutions of the following Kirchhoff equation -M(integral(R)2|del u|(2)dx)Delta u=lambda u+b(x)f(u),x is an element of R-2, with L-2-constraint integral(R)2u(2)dx=a, where a>0, M is an element of C([0,+infinity)), lambda is an element of R is a Lagrange multiplier, the potential b is an element of C-1(R-2,(0,infinity)) and the nonlinearity f is an element of C(R,R) satisfies the critical exponential growth at infinity in the sense of the Trudinger-Moser inequality and the mass supercritical growth at the origin. By virtue of the variational approach, we prove the existence of ground state normalized solutions to the problem above for any a>0.