Nodal solutions for fractional elliptic equations involving exponential critical growth

In the present paper, we study the existence of least energy nodal solution for a Dirichlet problem driven by the 12−Laplacian operator of the following type: (−Δ)12u+V(x)u=f(u)in(a,b),u=0inR∖(a,b), where V:[a,b]→[0,+∞) is a continuous potential and f(t) is a nonlinearity that grows like exp(t2) as t→+∞. By using the constraint variational method and quantitative deformation lemma, we obtain a least energy nodal solution u for the given problem. Moreover, we show that the energy of u is strictly larger than twice the ground state energy.