Sahoo, Alok Kumar and Manna, Bhakti Bhusan
(2019)
On A Singularly Perturbed Anisotropic Elliptic System with Neumann Boundary Data.
arXiv.org.
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Abstract
In this article we have described the role of the coefficients a(x), b(x) and c(x) to determine the concentration profile of the positive least energy solutions to the following anisotropic elliptic system:
−ε 2∆u + c(x)u = b(x)v q , and − ε 2∆v + c(x)v = a(x)u p in Ω
u > 0, v > 0 in Ω, and ∂u ∂ν = 0 = ∂v ∂ν on ∂Ω
Ω is a smooth bounded domain in R n , and n ≥ 3. As a consequence of this result, we have also shown the existence of some higher dimensional concentrating solutions for some singularly perturbed elliptic systems.
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