TY - JOUR
T1 - Exactly two positive solutions of nonhomogeneous semilinear elliptic equations in the half-space
AU - Hsu, Tsing San
PY - 2008/12/15
Y1 - 2008/12/15
N2 - In this article, we shall show that under suitable conditions on f and h, there exists a positive number λ* such that the nonhomogeneous semilinear elliptic equation - Δ u + σ2 u = λ (f (u) + h (x)) in R+N, u ∈ H01 (R+N), N ≥ 3, has exactly two positive solutions if λ ∈ (0, λ*), a unique positive solution if λ = λ* and no positive solution if λ > λ*. We also obtain some properties of the set of solutions.
AB - In this article, we shall show that under suitable conditions on f and h, there exists a positive number λ* such that the nonhomogeneous semilinear elliptic equation - Δ u + σ2 u = λ (f (u) + h (x)) in R+N, u ∈ H01 (R+N), N ≥ 3, has exactly two positive solutions if λ ∈ (0, λ*), a unique positive solution if λ = λ* and no positive solution if λ > λ*. We also obtain some properties of the set of solutions.
KW - Exactly two positive solutions
KW - Nonhomogeneous
KW - Semilinear elliptic equations
KW - The half-space
UR - http://www.scopus.com/inward/record.url?scp=55049101327&partnerID=8YFLogxK
U2 - 10.1016/j.na.2007.10.055
DO - 10.1016/j.na.2007.10.055
M3 - 文章
AN - SCOPUS:55049101327
SN - 0362-546X
VL - 69
SP - 4324
EP - 4339
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 12
ER -