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In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term  − div g 2 u ∇ u + g u g ′ u ∇ u 2 + V x u = λ x − μ ∗ u p u p − 2 u , x ∈ ℝ N , where  N ≥ 3 ,  g : ℝ → ℝ + is a  C 1 even function,  g 0 = 1 ,  g ′ s ≥ 0 is for all  s ≥ 0 ,  lim ∣ s ∣ → + ∞ g s / s α − 1 ≔ β &gt; 0 is for some  α &gt; 1 , and  α − 1 g s ≥ g ′ s s is for all  s ≥ 0 ,  2 α ≤ p ≤ 2 α N − μ / N − 2 , and  0 &lt; μ &lt; N . We prove that the equation admits a solution by using a constrained minimization argument.

An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term