Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (3): 909-924.doi: 10.1016/S0252-9602(11)60285-3

• Articles • Previous Articles     Next Articles

MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

 ZHANG Yi-Min, SHEN Yao-Tian   

  • Received:2009-07-13 Revised:2010-03-03 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    Project supported by the National Science Foundation of China (10771074;  10801055) and  Doctoral Program of NEM of China (200805611026).

Abstract:

In this article, under some conditions on the behaviors of the perturbed function f(x, s) or its primitive F(x, s)=∫0s f(x, t)dt near infinity and near zero, a class of asymptotically linear elliptic equations involving natural growth term is studied. By computing the critical group, the existence of three nontrivial solutions is proved.

Key words: critical group, weak slope, singular homology group, non-smooth Morse theory

CLC Number: 

  • 35J20
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