Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights
We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu−(μ/|x|2)u=λf(x)|u|q−2u+g(x)|u|2∗−2u in Ω, u=0 on ∂Ω, where 0∈&#...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2009/584203 |
| Summary: | We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu−(μ/|x|2)u=λf(x)|u|q−2u+g(x)|u|2∗−2u in Ω, u=0 on ∂Ω, where 0∈Ω⊂ℝN(N≥3) is a bounded domain with smooth boundary ∂Ω, λ>0, 0≤μ<μ¯=(N−2)2/4, 2∗=2N/(N−2), 1≤q<2, and f, g are continuous functions on Ω¯ which are somewhere positive but which may change sign on Ω. |
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| ISSN: | 1687-2762 1687-2770 |