TY - JOUR
T1 - Existence of singular positive solutions for some semilinear elliptic equations
AU - Guo, Zongming
AU - Ye, Dong
AU - Zhou, Feng
PY - 2008/5
Y1 - 2008/5
N2 - We study positive solutions of an equation with singular nonlinearities. The equation arises in the study of equilibrium states of thin films. Under weak assumptions on the nonlinearity, we show that for N ≥ 3 there exists a family of radial solutions {uα}α>0 with uα (0) = α and each of them is oscillatory in (0,∞). We obtain then a singular radial solution in (0,∞) by taking the limit α → 0. Meanwhile, using the solutions obtained in (0,∞), we show some existence results for the corresponding Neumann eigenvalue problem on a ball.
AB - We study positive solutions of an equation with singular nonlinearities. The equation arises in the study of equilibrium states of thin films. Under weak assumptions on the nonlinearity, we show that for N ≥ 3 there exists a family of radial solutions {uα}α>0 with uα (0) = α and each of them is oscillatory in (0,∞). We obtain then a singular radial solution in (0,∞) by taking the limit α → 0. Meanwhile, using the solutions obtained in (0,∞), we show some existence results for the corresponding Neumann eigenvalue problem on a ball.
KW - Elliptic equation with singular nonlinearity
KW - Oscillation
KW - Rupture solutions
UR - https://www.scopus.com/pages/publications/62749163109
U2 - 10.2140/pjm.2008.236.57
DO - 10.2140/pjm.2008.236.57
M3 - 文章
AN - SCOPUS:62749163109
SN - 0030-8730
VL - 236
SP - 57
EP - 71
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -