Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in ℝ𝑁
Existence and multiplicity of positive solutions for the following semilinear elliptic equation: −Δ𝑢+𝑢=𝑎(𝑥)|𝑢|𝑝−2𝑢+𝜆𝑏(𝑥)|𝑢|𝑞−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), are established, where 𝜆>0,1<𝑞<2<𝑝<2∗(2∗=2𝑁/(𝑁−2) if 𝑁≥3,2∗=∞ if 𝑁=1,2), 𝑎, 𝑏 satisfy suitable conditions, and 𝑏 maybe changes sign in ℝ𝑁....
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/864296 |
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