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Existence and Concentration Behavior of Ground States for a Generalized Quasilinear Choquard Equation Involving Steep Potential Well

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Abstract

In this paper, we consider the following generalized quasilinear Choquard equation with steep potential well

$$\begin{aligned} -\text {div}(g^{2}(u)\nabla u)+g(u)g^{\prime }(u)|\nabla u|^{2}+\lambda V(x)u=(I_{\alpha }*F(u))f(u), \ x \in {\mathbb {R}}^{N}, \end{aligned}$$

where \(N\ge 3\), \(\alpha \in (0,N)\), \(\lambda >0\) is a parameter and \(I_{\alpha }\) is the Riesz potential. Under some appropriate assumptions on g, V(x) and f, we prove the existence of ground states and obtain the concentration behavior of the solutions when \(\lambda \) is large enough via variational methods.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11901276 and 11961045), and supported partly by the Provincial Natural Science Foundation of Jiangxi, China (Nos. 20202BAB201001 and 20202BAB211004).

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  1. School of Mathematics and Computer Sciences, Nanchang University, Nanchang, Jiangxi, 330031, People’s Republic of China

    Yixuan Wang & Xianjiu Huang

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  1. Yixuan Wang
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Wang, Y., Huang, X. Existence and Concentration Behavior of Ground States for a Generalized Quasilinear Choquard Equation Involving Steep Potential Well. Bull. Iran. Math. Soc. 49, 9 (2023). https://doi.org/10.1007/s41980-023-00756-w

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