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Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in â„ ð ‘

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  • Tsing-San Hsu

Abstract

Existence and multiplicity of positive solutions for the following semilinear elliptic equation: − Δ ð ‘¢ + ð ‘¢ = ð ‘Ž ( ð ‘¥ ) | ð ‘¢ | ð ‘ âˆ’ 2 ð ‘¢ + 𠜆 ð ‘ ( ð ‘¥ ) | ð ‘¢ | ð ‘ž − 2 ð ‘¢ in â„ ð ‘ , ð ‘¢ ∈ ð » 1 ( â„ ð ‘ ) , are established, where 𠜆 > 0 , 1 < ð ‘ž < 2 < ð ‘ < 2 ∗ ( 2 ∗ = 2 ð ‘ / ( ð ‘ âˆ’ 2 ) if ð ‘ â‰¥ 3 , 2 ∗ = ∞ if ð ‘ = 1 , 2 ) , ð ‘Ž , ð ‘ satisfy suitable conditions, and ð ‘ maybe changes sign in â„ ð ‘ . The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold.

Suggested Citation

  • Tsing-San Hsu, 2011. "Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in â„ ð ‘," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, June.
    • Handle: RePEc:hin:jnlaaa:864296
    DOI: 10.1155/2011/864296
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