NONDEGENERACY

作品数：8被引量：2H指数：1
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Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations
《Acta Mathematicae Applicatae Sinica》2025年第2期414-424,共11页Yu-ting KANG Peng LUO Chang-lin XIANG Xue-xiu ZHONG 
partially supported by National Natural Science Foundation of China(Nos.12171183,11831009);the Fundamental Research Funds for the Central Universities(Nos.KJ02072020-0319,CCNU22LJ002);financially supported by National Natural Science Foundation of China(No.12271296);partially supported by National Natural Science Foundation of China(No.11801581);Guangdong Basic and Applied Basic Research Foundation(2021A1515010034);Guangzhou Basic and Applied Basic Research Foundation(202102020225);Province Natural Science Fund of Guangdong(2018A030310082).
In the present paper,we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations-M(∫_(R^(N))|∇_(v)|^(2)dx)Δ^(v)=g(v)in R^(N);where M:[0;+∞)→R is a continuous function satisf...
关键词：Kirchhoff type equations general nonlinearities UNIQUENESS NONDEGENERACY singular perturbation problem 
Nondegeneracy of eigenvectors and singular vector tuples of tensors
《Science China Mathematics》2022年第12期2483-2492,共10页Shenglong Hu 
supported by National Natural Science Foundation of China(Grant No.11771328);Young Elite Scientists Sponsorship Program by Tianjin and the Natural Science Foundation of Zhejiang Province of China(Grant No.LD19A010002)。
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singul...
关键词：tensor singular vector tuple EIGENVECTOR Z-eigenvector NONDEGENERACY generic 
Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions
《Frontiers of Mathematics in China》2020年第3期571-591,共21页Kun WANG Junxiang XU 
This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11871146,11671077);the Innovation Project for college postgraduates in Jiangsu Province(No.KYZZ160113).
We consider a class of analytic area-preserving mappings Cm-smoothly depending on a parameter.Without imposing on any non-degeneracy assumption,we prove a formal KAM theorem for the mappings,which implies many previou...
关键词：Area-preserving mapping invariant curve KAM iteration nondegeneracy condition 
Asymptotic Behaviour of Hessian Equation with Boundary Blow Up
《Acta Mathematicae Applicatae Sinica》2017年第3期575-586,共12页Lei-na ZHAO Zi-jian LIU 
Supported,in part,by the National Natural Science Foundation of China(No.11401060);the science and Technology Research program of Chongqing Municipal Education Commission(Grant NO.KJ 1705136)
We consider the boundary blow up problem for k-hessian equation with nonlinearities of power and of exponential type, and prove their existence, uniqueness and asymptotic behaviour. Moreover we also show that their pe...
关键词：boundary blowup problem NONDEGENERACY k-hessian equation 
Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry
《Advances in Pure Mathematics》2014年第4期103-107,共5页Yong Liu Jun Wang 
The Allen-Cahn equation on the plane has a 6-end solution U with regular triangle symmetry. The angle between consecutive nodal lines of U is . We prove in this paper that U is non-degenerated in the class of function...
关键词：Allen-Cahn Equation Multiple-End SOLUTION NONDEGENERACY 
NONDEGENERACY OF POSITIVE SOLUTIONS TO HOMOGENEOUS SECOND-ORDER DIFFERENTIAL SYSTEMS AND ITS APPLICATIONS被引量：1
《Acta Mathematica Scientia》2009年第2期435-446,共12页戴求亿 Christopher C. Tisdell 
supported by the NNSF of China(10671064);the second author was supported by the Australian Research Council's Discovery Projects(DP0450752)
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and ...
关键词：Second ordinary differential system Dirichlet problem positive solution NONDEGENERACY multiplicity result 
Existence and uniqueness of positive solutions of semilinear elliptic equations被引量：1
《Science China Mathematics》2007年第8期1141-1156,共16页Qiu-yi DAI Yu-xia FU Yong-geng GU 
the National Natural Science Foundation of China(Grant Nos.10671064,10171029)
This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to pro...
关键词：semilinear elliptic equation positive solution EXISTENCE UNIQUENESS NONDEGENERACY 35J65 
Arnold's theorem on properly degenerate systems with the Russmann nondegeneracy
《Science China Mathematics》2005年第12期1656-1669,共14页HAN Yuecai LI Yong 
supported by the National Outstanding Young’s Award of China;National 973 Project of China:Nonlinearity;Specialized Research Fund for the Doctoral Program of Higher Education and the Young Teacher's Foundation of Jilin University;supported by 985 Project of Jilin University.
In this paper, we investigate the persistence of invariant tori for the nearly in-tegrable Hamiltonian system H(x,y) = h(y) + εp(x,y) + ε2Q(x,y), where h(y) and εp(x,y) satisfy the Russmann non-degenerate condition...
关键词：Arnold's theorem the Russmann non-degenerate condition. 
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