Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weighted ð ‘ ( ð ‘¥ ) -Laplacian Equations with Exponential Nonlinearities

Li Yin, Yunrui Guo, Jing Yang, Bibo Lu and Qihu Zhang

Abstract and Applied Analysis, 2010, vol. 2010, 1-20

Abstract:

This paper investigates the following ð ‘ ( ð ‘¥ ) -Laplacian equations with exponential nonlinearities: − Δ ð ‘ ( ð ‘¥ ) ð ‘¢ + 𠜌 ( ð ‘¥ ) ð ‘’ ð ‘“ ( ð ‘¥ , ð ‘¢ ) = 0 in Ω , ð ‘¢ ( ð ‘¥ ) → + ∞ as ð ‘‘ ( ð ‘¥ , 𠜕 Ω ) → 0 , where − Δ ð ‘ ( ð ‘¥ ) ð ‘¢ = − d i v ( | ∇ ð ‘¢ | ð ‘ ( ð ‘¥ ) − 2 ∇ ð ‘¢ ) is called ð ‘ ( ð ‘¥ ) -Laplacian, 𠜌 ( ð ‘¥ ) ∈ ð ¶ ( Ω ) . The asymptotic behavior of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:971268

DOI: 10.1155/2010/971268

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