Normalized solutions to p-Laplacian equations with combined nonlinearities

doi:10.1088/1361-6544/ac902c

	Normalized solutions to p-Laplacian equations with combined nonlinearities
	Zhang, Zexin 2; Zhang, Zhitao 1,2,3
刊名	NONLINEARITY
	2022-11-03
卷号	35 期号:11 页码:5621-5663
关键词	normalized solutions p-Laplacian equations critical point ground state Pohozaev identity
ISSN号	0951-7715
DOI	10.1088/1361-6544/ac902c
英文摘要	In this paper, we study the p-Laplacian equation with a L-p-norm constraint: {-Delta(p)u = lambda vertical bar u vertical bar(p-2)u + mu vertical bar u vertical bar(q-2)u + g(u) in R-N, integral(RN) vertical bar u vertical bar(p)dx = a(p), where N >= 2, a > 0, 1 < p < q <= (p) over bar := p + p(2)/N, mu is an element of R, g is an element of C(R, R) and lambda is an element of R is a Lagrange multiplier, which appears due to the mass constraint parallel to u parallel to(p) = a. We assume that g is odd and L-p-supercritical. When q < <(p)over bar> and mu > 0, we use Schwarz rearrangement and Ekeland variational principle to prove the existence of positive radial ground states for suitable p. When q = p and mu > 0 or q <= (p) over bar and mu <= 0, with an additional condition of g, we obtain a positive radial ground state if mu lies in a suitable range, by the Schwarz rearrangement and minimax theorems. Via a fountain theorem type argument, with suitable mu is an element of R, we obtain infinitely many radial solutions for any N >= 2 and establish the existence of infinitely many nonradial sign-changing solutions for N = 4 or N >= 6. In any case mentioned above, the range of mu depends on the value of a: vertical bar mu vertical bar can be large if a > 0 is small.
资助项目	National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12026217] ; National Natural Science Foundation of China[11871302]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	IOP Publishing Ltd
WOS记录号	WOS:000868891000001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60779]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhitao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 2.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Zexin,Zhang, Zhitao. Normalized solutions to p-Laplacian equations with combined nonlinearities[J]. NONLINEARITY,2022,35(11):5621-5663.
APA	Zhang, Zexin,&Zhang, Zhitao.(2022).Normalized solutions to p-Laplacian equations with combined nonlinearities.NONLINEARITY,35(11),5621-5663.
MLA	Zhang, Zexin,et al."Normalized solutions to p-Laplacian equations with combined nonlinearities".NONLINEARITY 35.11(2022):5621-5663.