期刊论文详细信息
Advances in Nonlinear Analysis | |
Multiple solutions for a Kirchhoff-type equation with general nonlinearity | |
article | |
Sheng-Sen Lu1  | |
[1] Center for Applied Mathematics, Tianjin University;Chern Institute of Mathematics and LPMC, Nankai University | |
关键词: Kirchhoff-type equation; Berestycki–Lions-type nonlinearity; multiplicity results; variational methods; | |
DOI : 10.1515/anona-2016-0093 | |
学科分类:社会科学、人文和艺术(综合) | |
来源: De Gruyter | |
【 摘 要 】
This paper is devoted to the study of the following autonomous Kirchhoff-type equation: -M(∫ℝN|∇u|2)Δu=f(u),u∈H1(ℝN),-M\biggl{(}\int_{\mathbb{R}^{N}}|\nabla{u}|^{2}\biggr{)}\Delta{u}=f(u),\quad u% \in H^{1}(\mathbb{R}^{N}), where M is a continuous non-degenerate function and N≥2{N\geq 2}. Under suitable additional conditions on M and general Berestycki–Lions-type assumptions on the nonlinearity of f , we establish several existence results of multiple solutions by variational methods, which are also naturally interpreted from a non-variational point of view.
【 授权许可】
CC BY
【 预 览 】
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