Existence and multiplicity of solutions for generalized quasilinear Schrödinger equations. Issue 10 (3rd October 2022)

• Record Type: Journal Article
• Authors: Gui, Xue-Lin; Ge, Bin
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 10(2022)
• Page Start: 2360
• Page End: 2381
• Publication Date: 2022-10-03
• Subjects: Quasilinear Schrödinger equations -- multiple solutions -- Ekeland's variational principle -- Ambrosetti–Rabinowitz condition; 35J20 -- 35J62 -- 35J66; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1924155
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We consider the generalized quasilinear Schrödinger equations (P) − d i v ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = λ f ( x, u ), x ∈ R N, where N ≥ 3, g : R → R + is an even differentiable function, f : R N × R → R satisfies the Carathéodory condition, the potential V ( x ) : R N → ( 0, ∞ ) is continuous and λ is a parameter. The intention of the article is to determine the precise positive interval of λ when the problem possesses at least two nontrivial solutions. The main tool is the abstract critical point which is based on the Ekeland variational principle. Moreover, the existence of one solution and infinite solutions has been studied by the mountain pass theorem and the symmetric mountain pass theorem.