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 the1 2 − Laplacian operator of the following type:( − Δ )1 2u + V ( x ) u = f ( u )in ( a , b ) ,u = 0in R ∖ ( a , b ) ,where V : [ a , b ] → [ 0 , + ∞ ) is a continuous potential and f ( t ) is a nonlinearity that grows like exp ( t 2 ) 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.