TY - JOUR
T1 - Existence of positive nonradial solutions for nonlinear elliptic equations in annular domains
AU - Lin, Song-Sun
PY - 1992/1/1
Y1 - 1992/1/1
N2 - We study the existence of positive nonradial solutions of equation Δu + f(u) = 0 in Ωa , u = 0 on ∂Ωa, where Ωa= x ϵ ℛn : a < x < 1 is an annulus in R , n ≥ 2 , and f is positive and superlinear at both 0 and ∞ . We use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak ϵ (0, 1) for any positive integer k if f is subcritical and for large k if f is supercritical. When f is subcritical, then a Nehari-type variational method can be used to prove that there exists a⋆ ϵ (0, 1) such that for any a ϵ a⋆ , 1, the equation has a nonradial solution on Ωa .
AB - We study the existence of positive nonradial solutions of equation Δu + f(u) = 0 in Ωa , u = 0 on ∂Ωa, where Ωa= x ϵ ℛn : a < x < 1 is an annulus in R , n ≥ 2 , and f is positive and superlinear at both 0 and ∞ . We use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak ϵ (0, 1) for any positive integer k if f is subcritical and for large k if f is supercritical. When f is subcritical, then a Nehari-type variational method can be used to prove that there exists a⋆ ϵ (0, 1) such that for any a ϵ a⋆ , 1, the equation has a nonradial solution on Ωa .
KW - Bifurcation method
KW - Nonradial solution
KW - Variational method
UR - http://www.scopus.com/inward/record.url?scp=84968484623&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1992-1055571-1
DO - 10.1090/S0002-9947-1992-1055571-1
M3 - Article
AN - SCOPUS:84968484623
VL - 332
SP - 775
EP - 791
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 2
ER -