TY - JOUR
T1 - Large solutions of elliptic equations with a weakly superlinear nonlinearity
AU - Cîrstea, Florica Corina
AU - Du, Yihong
PY - 2007/12
Y1 - 2007/12
N2 - This paper studies the asymptotic behavior near the boundary for large solutions of the semilinear equation Δu + au = b(x)f(u) in a smooth bounded domain Ω of ℝN with N ≥ 2, where a is a real parameter and b is a nonnegative smooth function on Ω̄. We assume that f(u) behaves like u(ln u)α as u → ∞, for some α > 2. It turns out that this case is more difficult to handle than those where f(u) grows like u p (p > 1) or faster at infinity. Under suitable conditions on the weight function b(x), which may vanish on ∂Ω, we obtain the first order expansion of the large solutions near the boundary. We also obtain some uniqueness results.
AB - This paper studies the asymptotic behavior near the boundary for large solutions of the semilinear equation Δu + au = b(x)f(u) in a smooth bounded domain Ω of ℝN with N ≥ 2, where a is a real parameter and b is a nonnegative smooth function on Ω̄. We assume that f(u) behaves like u(ln u)α as u → ∞, for some α > 2. It turns out that this case is more difficult to handle than those where f(u) grows like u p (p > 1) or faster at infinity. Under suitable conditions on the weight function b(x), which may vanish on ∂Ω, we obtain the first order expansion of the large solutions near the boundary. We also obtain some uniqueness results.
UR - http://www.scopus.com/inward/record.url?scp=58449097569&partnerID=8YFLogxK
U2 - 10.1007/s11854-008-0008-6
DO - 10.1007/s11854-008-0008-6
M3 - Article
SN - 0021-7670
VL - 103
SP - 261
EP - 277
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -