Generalized quasilinear Schrödinger equations with critical growth. (March 2017)

• Record Type: Journal Article
• Authors: Cheng, Yongkuan; Shen, Yaotian
• Is Part Of: Applied mathematics letters. Volume 65(2017:Mar.)
• Page Start: 106
• Page End: 112
• Publication Date: 2017-03
• Subjects: Quasilinear Schrödinger equations -- Mountain Pass Theorem -- Critical growth; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.10.011
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We establish the existence of nontrivial solutions for the following quasilinear Schrödinger equation: − Δ u + V ( x ) u − Δ [ l ( u 2 ) ] l ′ ( u 2 ) u = u α 2 ∗ − 1 + f ( u ), x ∈ R N, where V ( x ) : R N → R is a given potential and l, f are real functions, 2 ∗ = 2 N ∕ ( N − 2 ), N ≥ 3 . Our results cover two physical models l ( s ) = s α 2, l ( s ) = ( 1 + s ) α 2, α > 1 and recent results from the literature (Shen and Wang, 2016, Deng et al., 2016) are improved and extended.