Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator

Article type: Research Article

Authors: Tao, Huo^a | Li, Lin^{a; *} | Yang, Xiao-Qiong^b

Affiliations: [a] School of Mathematics and Statistics & Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing 400067, China | [b] School of Foreign Languages, Chongqing Technology and Business University, Chongqing 400067, China

Correspondence: [*] Corresponding author. E-mails: [email protected], [email protected].

Abstract: In this paper, we study the existence results of a quasilinear elliptic problem involving the 1-biharmonic operator in RN, whose nonlinearity satisfies appropriate conditions. The existence theorem is proved through a new version of the Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais–Smale one.

Keywords: 1-biharmonic operator, BL space, Variational methods

DOI: 10.3233/ASY-221822

Journal: Asymptotic Analysis, vol. 133, no. 4, pp. 535-553, 2023