Normalized solutions and bifurcation for fractional Schrödinger equation with linear potential

In the paper, we consider the existence of normalized solutions for following fractional Schrödinger equation (FSE)(−Δ)su+V(x)u=K(x)f(u)+λu,inRNwhere N≥2, s∈(0,1), λ∈R is a parameter and (−Δ)s is the fractional Laplacian operator. We prove existence of normalized solutions for equation (FSE) under hypotheses on the potentials V and K. Moreover, we also obtain λ=0 is a bifurcation point.