TY - JOUR
T1 - Infinite multiplicity for an inhomogeneous supercritical problem in entire space
AU - Wang, Liping
AU - Wei, Juncheng
PY - 2013/5
Y1 - 2013/5
N2 - Let K(x) be a positive function in ℝN, N ≥ 3 and satisfy lim|x|→∞ K(x) = K∞ where K ∞ is a positive constant. When p > N+1/N-3, N ≥ 4, we prove the existence of infinitely many positive solutions to the following supercritical problem: Δu(x) + K(x)up = 0, u > 0 in ℝN, lim|x|→∞ u(x) = 0. If in addition we have, for instance, lim|x|→∞ |x|μ(K(x)- K∞) = C0 ≠ 0, 0 < μ ≤ N - 2p+2/p-1, then this result still holds provided that p > N+2/N-2.
AB - Let K(x) be a positive function in ℝN, N ≥ 3 and satisfy lim|x|→∞ K(x) = K∞ where K ∞ is a positive constant. When p > N+1/N-3, N ≥ 4, we prove the existence of infinitely many positive solutions to the following supercritical problem: Δu(x) + K(x)up = 0, u > 0 in ℝN, lim|x|→∞ u(x) = 0. If in addition we have, for instance, lim|x|→∞ |x|μ(K(x)- K∞) = C0 ≠ 0, 0 < μ ≤ N - 2p+2/p-1, then this result still holds provided that p > N+2/N-2.
KW - Entire space
KW - Infinite multiplicity
KW - Supercritical
UR - https://www.scopus.com/pages/publications/84873318445
U2 - 10.3934/cpaa.2013.12.1243
DO - 10.3934/cpaa.2013.12.1243
M3 - 文章
AN - SCOPUS:84873318445
SN - 1534-0392
VL - 12
SP - 1243
EP - 1257
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 3
ER -