Observe that if (fin W^{1,p}(mathbb {R}^n)) is nonnegative, spherically symmetric and decreasing, then there exists a decreasing function (uin W^{1,p}_{loc}(mathbb {R})) such that (f(x)=u(|x|)).
The experimental design is based on two central features: first, there exists a decreasing probability of surviving which implies an uncertain future income; and, secondly, there are two sequences of income, one when individual works and another when she is retired.
Then (2.1 - 2.2 2.1 - 2.2notone solution withas = c ∗. Proof If (3.3) or (3.4) holds, then there exists a decreasing sequence { c n } n = 1 ∞ with c n → c ∗, n → ∞ such that for each c n, (2.1)-(2.2) has a positive monotone solution ( ϕ 1 n, ϕ 2 n ).
Subjects make consumption and saving decisions in an environment with two central features: first, there exists a decreasing probability of survival; and second, in addition to the regular income they get while active, they receive a unique lump-sum payment when retired.
If we assume that M x ∖ U ( M s, ε ) ≠ ∅, then there exists a decreasing sequence of positive numbers { δ n } n = 1 ∞, lim n → ∞ δ n = 0 such that for each δ n, there exist points s n ∈ U ( x, δ n ) and x n ∈ M x ∖ U ( M s n, ε ) such that ρ ( x n, M s n ) > ε for each n ≥ 1.
Suppose that obeys (3.6) and obeys (3.7), then there exist a decreasing continuous function such that as and an increasing function such that as.
Then there exists a decreasing subsequence { α ℓ n } n ∈ N of { α n } n ∈ N 1.
Next let,, denote the family of plurisubharmonic functions defined on such that there exists a decreasing sequence,, that converges pointwise to on, as tends to, and (3.2).
