Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

Zonghu Xiu

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We consider the existence of multiple solutions of the singular elliptic problem -div (|x|-ap|∇ u|p-2∇ u)+|u|p-2u/|x|(a+1)p=f|u|r-2u+h|u|s-2u+|x|-bp*|u|p*-2u, u(x) → 0 as |x| → +∞, where x ∈ ℝN, 1 1, p* = Np/(N − pd), d = a + 1 − b. By the variational method and the theory of genus, we prove that the above‐mentioned problem has infinitely many solutions when some conditions are satisfied.

Date: 2012
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https://doi.org/10.1155/2012/806397

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:806397

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