Liouville-type theorems for stable solutions of Kirchhoff equations with exponential and superlinear nonlinearities. Issue 8 (3rd August 2019)

• Record Type: Journal Article
• Authors: Wei, Yunfeng; Chen, Caisheng; Song, Hongxue; Yang, Hongwei
• Is Part Of: Complex variables and elliptic equations. Volume 64:Issue 8(2019)
• Page Start: 1297
• Page End: 1309
• Publication Date: 2019-08-03
• Subjects: V. Rădulescu; Kirchhoff equation -- stable solutions -- nonexistence; 35J60 -- 35B53 -- 35B33 -- 35B45; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2018.1514030
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: In this paper we prove Liouville-type theorems for stable solutions of Kirchhoff equations (1) − a + b ∫ R N | ∇ u | 2 d x Δ u = h ( x ) e u, x ∈ R N, and (2) − a + b ∫ R N | ∇ u | 2 d x Δ u = h ( x ) | u | q − 1 u, x ∈ R N, where a > 0, b ≥ 0, q > 1 and the nonnegative function h ( x ) ∈ C ( R N ) such that h ( x ) ≥ c 0 | x | d as | x | ≥ R 0 with d >−2 and some constants R 0, c 0 > 0 . Under suitable conditions on h ( x ) and q, the nonexistence of stable solutions to Equations (0.1) and (0.2) are investigated.