Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (6): 1881-1888.doi: 10.1016/S0252-9602(10)60180-4

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FOUNTAIN THEOREM OVER CONES AND APPLICATIONS

 YAN Shu-Sen, YANG Jian-Fu   

  • Received:2010-04-22 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The first author is supported by ARC grant of Australia; the second author is supported by National Natural Sciences Foundations of China (10961016 and 10631030); NSF of Jiangxi (2009GZS0011).

Abstract:

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem
{ -Δp u =λ |u|q-2u +μ |uγ-2u,       x∈Ω,
 u = 0,                                             x∈∂Ω,                (1)
 to show that problem (1) possesses infinitely many solutions, where 1<p<N, 1< q <p < γ, Ω(RN is a smooth bounded domain and λ,μ∈R.

Key words: fountain theorem over cones, infinitely , many solutions, quasilinear elliptic problem

CLC Number: 

  • 35J60
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