Abstract
In this paper, we study the generalized quasilinear Schrödinger equation
where \(N\ge 3\), \(0<\alpha <N\), \(\frac{2(N+\alpha )}{N}< p<\frac{2(N+\alpha )}{N-2}\), \(V: {{\mathbb {R}}}^N\rightarrow {{\mathbb {R}}}\) is a potential function and \(I_{\alpha }\) is a Riesz potential. Under appropriate assumptions on g and V(x), we establish the existence of positive solutions and ground state solutions.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11661053, 11771198, 11961045, and 11901276), the Provincial Natural Science Foundation of Jiangxi (Grant Nos. 20161BAB201009, 20181BAB201003, 20202BAB201001 and 20202BAB211004), the Outstanding Youth Scientist Foundation Plan of Jiangxi (Grant No. 20171BCB23004).
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Communicated by Amin Esfahani.
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Ling, P., Huang, X. & Chen, J. Some Existence Results on a Class of Generalized Quasilinear Schrödinger Equations with Choquard Type. Bull. Iran. Math. Soc. 48, 1389–1411 (2022). https://doi.org/10.1007/s41980-021-00585-9
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DOI: https://doi.org/10.1007/s41980-021-00585-9