where the MathML source">α(−Δ) with α ∈ (0, 1) is the fractional Laplace operator defined as a pseudo-differential operator with the symbol |ξ|2α, V(x) is a positive potential function and the nonlinearity f is saturable, that is, the MathML source">f(u)/u→l∈(0,+∞) as the MathML source">|u|→+∞. By using a variant version of Mountain Pass Theorem, we prove that there exists a bound state and ground state of (P) when V and f satisfy suitable assumptions.
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