| 21 | 0 | 16 |
| 下载次数 | 被引频次 | 阅读次数 |
研究了一类Schrdinger算子的特征值问题.使用变分法得到的研究结果表明,当其位势满足一定条件时,该算子存在唯一的特征值λ有一个正的特征函数.此外,该算子的所有其它特征值都小于λ且它们所对应的特征函数都变号.
Abstract：The eigenvalue problem of a Schrdinger operator is studied.By the variational methods,Results show that there exists an unique eigenvalua having a positive eigenfunction when the potential of the operator satisfies some conditions.Furthermore,all other eigenvalues of this operator are less than and their eigenfunctions change sign.
[1]Strauss W A.Existence of solitary waves in higher dimensions[J].Comm.Math.Phys.,1977,55(2):149-162.
[2]Berestycki H,Lions P L.Nonlinear scalar field equations,I.Existence of a ground state[J].Arch.Ration.Mech.Analysis,1983,82(4):313-346.
[3]Berestycki H,Lions P L.Nonlinear scalar field equations,II.Existence of infinitely many solutions[J].Arch.Ration.Mech.Analysis,1982,82(4):347-376.
[4]Rabinowitz P H.On a class of nonlinear Schrdinger equa-tions[J].Z.Angew Math.Phys.,1992,43:270-290.
[5]Stuart C A,Zhou Huansong.Positive eigenfunctions of aSchrdinger operator[J].J.London Math.Soc.,2005,72(2):429-441.
[6]Stuart C A,Zhou Huansong.Global branch of solutions fornonlinear Schrdinger equations with deepening potentialwell[J].Proc.London Math.Soc.,2006,92(3):655-681.
[7]万优艳.一类Schrdinger算子的正特征函数[J].江汉大学学报:自然科学版,2009,37(4):9-10.
[8]Stuart C A.An introduction to elliptic equations on RN[C]//Ambrosetti A.,Chang K C,Ekeland I.Nonlinear Func-tional Analysis and Applications to Differential Equations.Singapore:World Scientific,1998.
[9]Misra J C.Applicable mathematics in the golden age[M].New Delhi:Narosa Publishing House,2003:1-31.
基本信息:
DOI：
中图分类号:O177
引用信息:
[1]万优艳.一类Schrdinger算子的正特征函数的探讨[J].南通大学学报(自然科学版),2010,9(04):75-77.
基金信息:
湖北省教育厅科研计划青年项目(Q20083401)