Ground state solutions for a quasilinear Schrodinger equation with singular coefficients

Abstract

<p>In this article, we study the quasilinear Schrodinger equation with the critical exponent and singular coefficients,</p> <pre>-∆u + V(x)u - ∆(|u|²)u = λ |u|^q-2u / |x|^μ + |u|^22*(v)-2u / |x|^v in ℝ^N,</pre> <p>where N ≥ 3, 2 < q < 22*(μ), 2*(s) = 2<N-s) / N-2, and λ, μ, v are parameters with λ > 0, μ, v ∈ [0, 2). By applying the Mountain Pass Theorem and the Concentration Compactness Principle, we establish the existence of the ground state solutions to the above problem.</p>