Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (5): 1144-1150.

• Articles • Previous Articles     Next Articles

Existence of Positive Solutions to Semilinear Elliptic Equations with Bi-Parameter and a Threshold Result

 YAO Xian-Zhong, MU Chun-Lai, ZHANG Fu-Chen   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331;College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing |400067
  • Received:2013-03-27 Revised:2014-04-19 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    中央高校基金(CDJXS11100039)资助.

Abstract:

We investigate the existence and nonexistence of the positive solution to a semilinear elliptic problem with bi-parameter
under Robin condition. More precisely, we admit that there exists a λ*=λ*(c)<∞, for  any given boundary parameter 0<c<∞),  such that the problem has a minimum solutions for 0<λ≤λ*, whereas, any other solution is an initial datum threshold for the existence and nonexistence of global solution to the parabolic version.

Key words: Semilinear elliptic problem, Positive solution, Bi-parameter, Threshold result

CLC Number: 

  • 35B35
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