THE HENON EQUATION WITH A CRITICAL EXPONENT UNDER THE NEUMANN BOUNDARY CONDITION

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For n >= 3 and p = (n+2)/(n- 2), we consider the Henon equation with the homogeneous Neumann boundary condition -Delta u + u = vertical bar x vertical bar(alpha) u(p), u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega subset of B(0,1) subset of R-n, n >= 3, alpha >= 0 and partial derivative*Omega partial derivative Omega boolean AND partial derivative B(0, 1) not equal empty set. It is well known that for alpha = 0, there exists a least energy solution of the problem. We are concerned on the existence of a least energy solution for alpha > 0 and its asymptotic behavior as the parameter a approaches from below to a threshold alpha(0) is an element of (0, infinity] col for existence of a least energy solution.
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Issue Date
2018-09
Language
English
Article Type
Article
Citation

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.38, no.9, pp.4353 - 4390

ISSN
1078-0947
DOI
10.3934/dcds.2018190
URI
http://hdl.handle.net/10203/246165
Appears in Collection
MA-Journal Papers(저널논문)
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