Existence and Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Schrödinger Equations

In this paper, we study the quasilinear Schrödinger equation -Δ⁢u+V⁢(x)⁢u-γ2⁢(Δ⁢u2)⁢u=|u|p-2⁢u{-\Delta u+V(x)u-\frac{\gamma}{2}(\Delta u^{2})u=|u|^{p-2}u}, x∈ℝN{x\in\mathbb{R}^{N}}, where V⁢(x):ℝN→ℝ{V(x):\mathbb{R}^{N}\to\mathbb{R}} is a given potential, γ>0{\gamma>0}, and either p∈(2,2*){p\in...

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