Multiple solutions for a non-homogeneous elliptic equation at the critical exponent
2004 ◽
Vol 134
(1)
◽
pp. 69-87
◽
Keyword(s):
We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.
2011 ◽
Vol 63
(1-2)
◽
pp. 611-628
◽
2011 ◽
Vol 55
(1)
◽
pp. 155-166
◽
2011 ◽
Vol 141
(6)
◽
pp. 1279-1294
◽
2018 ◽
Vol 265
(9)
◽
pp. 4133-4157
◽
2009 ◽
Vol 11
(01)
◽
pp. 59-69
◽
2019 ◽
Vol 149
(5)
◽
pp. 1163-1173