On a Defocusing Quasilinear Schrödinger Equation with Singular Term

We consider a class of modified quasilinear Schrödinger equations −∆u + k2 u∆u2 + V (x)u = λa(x)u−α + b(x)uβ in RN, where N ≥ 3, V is a suitable non-negative continuous potential; a, b are bounded mensurable functions, 0 < α < 1 < β ≤ 2∗ − 1 and k, λ ≥ 0 are two parameters. We establish global existence and local multiplicity results of positive solutions in H1(RN) ∩ L∞(RN) for the equation with appropriate classes of parameters α, β and coefficients a(x), b(x). © 2023 American Institute of Mathematical Sciences. All rights reserved.