Multiple Positive Solutions for Semilinear Elliptic Equations in ℝ𝑁 Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions
We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation −Δ𝑢+𝑢=𝜆𝑎(𝑥)|𝑢|𝑞−2𝑢+𝑏(𝑥)|𝑢|𝑝−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), where 𝜆>0, 1<𝑞<2<𝑝<2∗(2∗=2𝑁/(𝑁−2) if 𝑁≥3, 2∗=∞ if 𝑁=1,2), 𝑎(𝑥), 𝑏(𝑥) satisfy suitable conditions, and 𝑎(𝑥) may change sign in ℝ𝑁...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/658397 |
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