Abstract
In this paper we study the existence and multiplicity of solutions for the critical fractional Schrödinger equationwhere ε and λ are positive parameters, 0 < α < 1, (−Δ)α denotes the fractional Laplacian of order α, N > 2α, is the fractional critical exponent; V is a positive continuous potential satisfying some conditions and f is a continuous subcritical nonlinear term. We prove that the equation has a nonnegative ground state solution and investigate the relation between the number of solutions and the topology of the set where V attains its minimum, for all sufficiently large λ and small ε.
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