Abstract
We consider the quasilinear Schrödinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the Pohozaev identity we get the existence results that generalize an earlier work [H. Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with a general nonlinearity, Commun. Pure Appl. Anal., 19(6):3429–3444, 2020] about the subcritical case to the critical case.
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The research is supported by National Natural Science Foundation of China (No. 11901499) and Nanhu Scholar Program for Young Scholars of XYNU (No. 201912).
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Han, JX., Chen, MC. & Xue, YF. Ground state solutions for quasilinear Schrödinger equations with critical Berestycki–Lions nonlinearities. Lith Math J 64, 138–162 (2024). https://doi.org/10.1007/s10986-024-09635-1
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DOI: https://doi.org/10.1007/s10986-024-09635-1