Infinitely many solutions to a class of quasilinear Schrödinger system in RN. (February 2016)

• Record Type: Journal Article
• Authors: Chen, Caisheng
• Is Part Of: Applied mathematics letters. Volume 52(2016:Feb.)
• Page Start: 176
• Page End: 182
• Publication Date: 2016-02
• Subjects: Quasilinear Schrödinger system -- Mountain pass lemma -- (PS) condition; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.09.007
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this work, we study the existence of multiple solutions to the quasilinear Schrödinger system of k equations − Δ p u j + a j ( x ) | u j | p − 2 u j = μ j | u j | q − 2 u j + 12 ∑ i ≠ j β i j | u i | m | u j | m − 2 u j, x ∈ R N, with u j ( x ) → 0 as | x | → ∞, j = 1, 2, …, k, and N ≥ 2, 1 < p < N, k ≥ 2, the potential a j ( x ) is positive and bounded in R N, μ j > 0, β i j = β j i for i ≠ j, j = 1, …, k . We develop a new technique to verify the ( P S ) condition and then apply a version of mountain pass lemma to prove the existence of infinitely many nonnegative solutions to the above system.