Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions
Let Ω∋0 be an-open bounded domain in ℝ𝑁(𝑁≥3) and 𝑝∗=(𝑝𝑁/(𝑁−𝑝)). We consider the following quasilinear elliptic system of two equations in 𝑊01,𝑝(Ω)×𝑊01,𝑝(Ω): −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢+(𝛼/(𝛼+𝛽))ℎ(𝑥)|𝑢|𝛼−2𝑢|𝑣|𝛽,−Δ𝑝𝑣=𝜇𝑔(𝑥)|𝑣|𝑞−2𝑣+(𝛽/(𝛼+𝛽))ℎ(𝑥)|𝑢|𝛼|𝑣|𝛽−2𝑣, where 𝜆,𝜇>0, Δ𝑝 denotes the 𝑝-Laplacian operator, 1≤𝑞...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/109214 |