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Some existence results on a class of generalized quasilinear Schr\”{o}dinger equations with Choquard type
  • Pingying Ling,
  • Xianjiu Huang,
  • Jianhua Chen
Pingying Ling
Nanchang University - Qianhu Campus
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Xianjiu Huang
Nanchang University - Qianhu Campus
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Jianhua Chen
central South university
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Abstract

{\bf Abstract.} In this paper, we study the generalized quasilinear Schr\”{o}dinger equation \begin{equation*} -\text{div}(g^2(u)\nabla u)+g(u)g’(u)|\nabla u|^2+V(x)u=(I_{\alpha}\ast|u|^{p})|u|^{p-2}u,\ \ \ x\in\R^N, \end{equation*} where $N\geq3$, $0<\alpha