We establish an existence theorem for a problem of the type ⎧⎪⎨ ⎪⎩ −Δpu + λ(x)|u|p−2u = f(x, u) + g(x, u) in RN lim |x|→+∞ u(x) = 0 where f, g : RN × R → R are Carth`eodory functions, λ ∈ L∞(Ω), with ess infΩλ > 0, and Δp is the p-Laplacian operator with p > N. This result extends to the case of RN a previous result related to a Neumann problem in bounded domains.
Existence results for nonlinear problems in R^N involving the p-Laplacian
RANIA F
2011-01-01
Abstract
We establish an existence theorem for a problem of the type ⎧⎪⎨ ⎪⎩ −Δpu + λ(x)|u|p−2u = f(x, u) + g(x, u) in RN lim |x|→+∞ u(x) = 0 where f, g : RN × R → R are Carth`eodory functions, λ ∈ L∞(Ω), with ess infΩλ > 0, and Δp is the p-Laplacian operator with p > N. This result extends to the case of RN a previous result related to a Neumann problem in bounded domains.File in questo prodotto:
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