Acta mathematica scientia, Series B >
TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONSTWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS
Received date: 2006-11-29
Online published: 2009-03-20
Supported by
Huang’s research is supported in part by NSFC (10471138), NSFC-NSAF (10676037), and 973 project of China (2006CB805902)
In this article, the author investigates some Hermite elliptic equations in a modified Sobolev space introduced by X. Ding [2]. First, the author shows the existence of a ground state solution of semilinear Hermite elliptic equation. Second, the author studies the eigenvalue problem of linear Hermite elliptic equation in a bounded or unbounded
domain.
Huang Feimin . TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONSTWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 409 -414 . DOI: 10.1016/S0252-9602(09)60040-0
[1] Ding X. On a class of functional inequalities. Mathematical Advancement (in Chinese), 1964, 7(1): 49–56
[2] Ding X. On a Modified Sobolev Space. Acta Mathematica Scientia, 2008, 28B(1): 1–6
[3] Ding X, Ding Y. Hermite expansions and generalized functions (In Chinese). China: Huazhong Normal
University Press, 2005
[4] Ding W, Ni W. On the existence of positive solutions of a semilinear elliptic equation. Arch Rat Mech
Anal, 1986, 91(4): 283–308
[5] Schoen R, Yau S. Lectures on differential geometry. Cambridge, MA: International Press, 1994
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