Potential well method for p(x)-Laplacian equations with variable exponent sources. (December 2020)

• Record Type: Journal Article
• Authors: Nhan, Le Cong; Chuong, Quach Van; Truong, Le Xuan
• Is Part Of: Nonlinear analysis. Volume 56(2020)
• Publication Date: 2020-12
• Subjects: p(x)-Laplacian -- Global existence -- Decay property -- Non-global existence -- Variable exponents; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103155
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study a class of semilinear p ( x ) -Laplacian equations with variable exponent sources. By using potential well method, we first prove a threshold results on the existence and nonexistence of global solutions to the equations when initial energy is less than the mountain pass level d . In the former case we also show the decay properties of energy functional. We finally obtain the non-global existence results with high energy initial data.