2019/10/23 by Alok kumar Sahoo, Sahoo, Alok kumar, Bhakti Bhusan Manna +1
Computer Science · Mathematics · #35J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Primary 35J47 #Secondary 35J57
paper · pdf · doi:10.48550/arxiv.1910.10354
openalex publication_date 2019/10/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this article we shall study the following elliptic system with\ncoefficients:\n \
notag\n
left
beginaligned\n -
epsilon2
Delta u +c(x)u=b(x)|v|q-1v, amp;
text and -
epsilon2
Delta v\n+c(x)v=a(x) |u|p-1u amp;amp;
textin
Omega
newline\n ugt;0,
vgt;0
text in
Omega, amp;
text and
quad
frac
partialν
partial
nu = 0 =
frac
partial v
partial
nu amp;amp;
texton
partial
Omega\n
endaligned\n
right.\n where \Ω is a smooth bounded domain in Rn, n\≥ 3.\nThe coefficients a(x), b(x) and c(x) are positive bounded smooth functions.\nWe shall study the existence of point concentrating solutions and discuss the\nrole of the coefficients to determine the concentration profile of the\nsolutions. We have also discussed some applications of our main theorem towards\nthe existence of solutions concentrating on higher-dimensional orbits.\n