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We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V. Under suitable assumptions on V, using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti–Rabinowitz type condition or monotonicity assumptions.

Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension