TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONSTWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS

doi:10.1016/S0252-9602(09)60040-0

Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (2): 409-414.doi: 10.1016/S0252-9602(09)60040-0

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TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONSTWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS

Huang Feimin

Institute of Applied Mathematics, AMSS, Academia Sinica, Beijing 100080, China

Received:2006-11-29 Online:2009-03-20 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.

Key words: Hermite elliptic equation, modified Sobolev space, eigenvalue problem

CLC Number:

35J60

Cite this article

Huang Feimin. TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONSTWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS[J].Acta mathematica scientia,Series B, 2009, 29(2): 409-414.

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References

[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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