Normalized solutions for the fractional P-Laplacian equation with exponential critical growth

In this paper, we investigate the existence of solution to the fractional p-Laplacian equation (-Delta)(p)(s)u + lambda divided by divided by u divided by divided by(p-2)u = f(u)in R-N, N >= 2, u is an element of W-s,W-p(R-N), satisfying the normalization constraint integral(RN)divided by u divided by(p)dx = c(p), where 0 < s < 1< p with sp = N. The nonlinearity f(t) has an exponential critical growth, i.e. behaves like exp(alpha|t|(N/(N-s))) for some alpha > 0 as |t|->infinity. Under some suitable conditions, we demonstrate the existence of the normalized ground state solution (via the constrained variational method) which is of mountain pass type. The proof is based on some minimax arguments and the Trudinger-Moser inequality in W-s,W-p(R-N).