Positive, negative, and sign-changing solutions to a quasilinear Schrödinger equation with a parameter
Abstract
In this paper, we study the following quasilinear Schrödinger equation with a parameter: −Δu+V(x)u−καΔ(|u|2α)|u|2α−2u=|u|p−2u+|u|(2α)2*−2u in RN, where N ≥ 3, α>12, 2 < p < (2α)2*, and κ is a positive constant. Under different assumptions on V, we obtain the existence of positive, negative, and sign-changing solutions. Our results generalize the results of Liu et al. [J. Differ. Equations 187, 473-493 (2003)] into the critical case for general α.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- December 2019
- DOI:
- 10.1063/1.5116602
- Bibcode:
- 2019JMP....60l1510Y