This paper is devoted to the following fractional relativistic Schrödinger equation: \((-\Delta+m^{2})^{s}u+V(x)u=f(x,u),\qquad x\in\mathbb{R}^{N},\) where (−Δ + m2)s is the fractional relativistic Schrödinger operator, s ∈ (0, 1), m > 0, V: ℝN → ℝ is a continuous potential and f: ℝN × ℝ → ℝ is a superlinear continuous nonlinearity with subcritical growth. We consider the case where the potential V is indefinite so that the relativistic Schrödinger operator (−Δ + m2)s + V possesses a finite-dimensional negative space. With the help of extension method and Morse theory, the existence of a nontrivial solution for the above problem is obtained.
