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Some existence results on a class of generalized quasilinear Schr\โ€{o}dinger equations with Choquard type

Some existence results on a class of generalized quasilinear Schr\โ€{o}dinger equations with Choquard type

{\bf Abstract.} In this paper, we study the generalized quasilinear Schr\โ€{o}dinger equation \begin{equation*} -\text{div}(g^2(u)\nabla u)+g(u)gโ€™(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