Infinitely many sign-changing solutions for system of p-Laplace equations in RN. (May 2019)

• Record Type: Journal Article
• Authors: Zhao, Junfang; Liu, Xiangqing; Liu, Jiaquan
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 113
• Page End: 142
• Publication Date: 2019-05
• Subjects: 35B05 -- 35B45 -- 58J70; System of p-Laplacian equations -- Sign-changing solution -- Truncation method -- Concentration analysis; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.12.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the system of p -Laplacian equations in R N − Δ p u j + μ j ( x ) | u j | p − 2 u j = ∑ i = 1 k β i j | u i | q | u j | q − 2 u j in R N, u j ( x ) → 0 as | x | → ∞, j = 1, …, k, where 1 < p < N, max { 2, p } < 2 q < p ∗ = N p N − p, β i j are constants, i, j = 1, …, k, β j j > 0, j = 1, 2, …, k, β i j ≤ 0, i ≠ j, i, j = 1, …, k ; μ j, j = 1, …, k are the potential functions and satisfy suitable decay assumptions. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration-compactness analysis on the approximating solutions.