The existence of multiple solutions for the Klein–Gordon equation with concave and convex nonlinearities coupled with Born–Infeld theory on R3. (December 2017)

• Record Type: Journal Article
• Authors: Chen, Shang-Jie; Song, Shu-Zhi
• Is Part Of: Nonlinear analysis. Volume 38(2017)
• Page Start: 78
• Page End: 95
• Publication Date: 2017-12
• Subjects: primary 35J61 -- secondary 35C06 35J20; Klein–Gordon equation -- Born–Infeld theory -- Concave and convex nonlinearities -- Ekeland's variational principle -- Mountain Pass Theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.04.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we prove the existence of multiple solutions for the following Klein–Gordon equation with concave and convex nonlinearities coupled with Born–Infeld theory { − Δ u + a ( x ) u − ( 2 ω + ϕ ) ϕ u = λ k ( x ) | u | q − 2 u + g ( x ) | u | p − 2 u, x ∈ R 3, Δ ϕ + β Δ 4 ϕ = 4 π ( ω + ϕ ) u 2, x ∈ R 3, where 1 < q < 2 < p < 6 . Under appropriate assumptions on a, k, g and λ, the existence of multiple nontrivial solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.