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NONTRIVIAL SOLUTIONS AND VARIATIONAL CHARACTERS OF POSITIVE HOMOGENEOUS ELLIPTIC EQUATION
Li, Chong1,2; Li, Shujie1
2017
Source PublicationJOURNAL OF NONLINEAR AND CONVEX ANALYSIS
ISSN1345-4773
Volume18Issue:7Pages:1265-1277
AbstractIn this paper we first study the solvability of the equation (0.1) {-Delta u = bu(+) + au(-) +t phi x is an element of Omega u = 0, x is an element of Omega by using Morse theory. If (a, b) is an element of Q(l)\Sigma, lambda(l) is simple and phi > 0, the connection between the numbers of the solutions and the location of (a, b) in Q(l) were established. Moreover, we give a complete expression for the behaviors of the reduced functional (J) over tilde ((a,b)) (v) as (a, b) locating in different regions divided by Schechter's curves. Since to find the critical points of (J) over tilde ((a,b)) (v) is equivalent to find the solutions of -Delta u = bu(+) + au(-), it is more convenient to deal with the problem which has been reduced to a finite dimensional space.
KeywordSolvability elliptic equation Morse theory reduced functional
Language英语
Funding ProjectNSFC[11471319] ; BCMIIS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000413881200004
PublisherYOKOHAMA PUBL
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29112
Collection数学所
Affiliation1.Acad Sinica, AMSS, Inst Math, Beijing 100190, Peoples R China
2.BCMIIS, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Li, Chong,Li, Shujie. NONTRIVIAL SOLUTIONS AND VARIATIONAL CHARACTERS OF POSITIVE HOMOGENEOUS ELLIPTIC EQUATION[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS,2017,18(7):1265-1277.
APA Li, Chong,&Li, Shujie.(2017).NONTRIVIAL SOLUTIONS AND VARIATIONAL CHARACTERS OF POSITIVE HOMOGENEOUS ELLIPTIC EQUATION.JOURNAL OF NONLINEAR AND CONVEX ANALYSIS,18(7),1265-1277.
MLA Li, Chong,et al."NONTRIVIAL SOLUTIONS AND VARIATIONAL CHARACTERS OF POSITIVE HOMOGENEOUS ELLIPTIC EQUATION".JOURNAL OF NONLINEAR AND CONVEX ANALYSIS 18.7(2017):1265-1277.
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