Abstract
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.
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Z. Liu is supported by the NSFC (11626127). M. Squassina is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). J. J. Zhang was partially supported by the Science Foundation of Chongqing Jiaotong University (15JDKJC-B033).
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Liu, Z., Squassina, M. & Zhang, J. Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension. Nonlinear Differ. Equ. Appl. 24, 50 (2017). https://doi.org/10.1007/s00030-017-0473-7
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DOI: https://doi.org/10.1007/s00030-017-0473-7