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Multiplicity of Solutions for Nonlocal Elliptic System of ( ð ‘ , ð ‘ž ) -Kirchhoff Type

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  • Bitao Cheng
  • Xian Wu
  • Jun Liu

Abstract

This paper is concerned with the following nonlocal elliptic system of ( p,q )-Kirchhoff type − [ ð ‘€ 1 ( ∫ Ω | ∇ ð ‘¢ | ð ‘ ) ] ð ‘ âˆ’ 1 Δ ð ‘ ð ‘¢ = 𠜆 ð ¹ ð ‘¢ ( ð ‘¥ , ð ‘¢ , ð ‘£ ) , in Ω, − [ ð ‘€ 2 ( ∫ Ω | ∇ ð ‘£ | ð ‘ž ) ] ð ‘ž − 1 Δ ð ‘ž ð ‘£ = 𠜆 ð ¹ ð ‘£ ( ð ‘¥ , ð ‘¢ , ð ‘£ ) , in Ω, ð ‘¢ = ð ‘£ = 0 , on 𠜕 Ω . Under bounded condition on M and some novel and periodic condition on F , some new results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by means of Bonanno's multiple critical points theorems without the Palais-Smale condition and Ricceri's three critical points theorem, respectively.

Suggested Citation

  • Bitao Cheng & Xian Wu & Jun Liu, 2011. "Multiplicity of Solutions for Nonlocal Elliptic System of ( ð ‘ , ð ‘ž ) -Kirchhoff Type," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, August.
    • Handle: RePEc:hin:jnlaaa:526026
    DOI: 10.1155/2011/526026
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