摘要
In this paper, we consider the following ODE problem { (-u"(τ)+(N-1)(N-3)/4τ^2 )u(τ)+λu(τ)=f(τ,τ(1-N)/2 u)u(τ),τ〉0, u∈H, N≥3. (P),where f ∈ C((0,+∞) ×R,R), f(τ,s) goes to p(τ) and q(τ) uniformly in τ 〉 0 as s→ 0 and s→+∞ respectively, 0≤ p(τ) ≤ q(τ) ∈L^∞(0,∞). Moreover, for τ 〉 0, f(τ, s) is nondecreasing in s≥ 0. Some existence and non-existence of positive solutions to problem (P) are proved without assuming that p(τ) = 0 and q(τ) has a limit at infinity. Based on these results, we get the existence of positive solutions for an elliptic problem.
In this paper, we consider the following ODE problem { (-u"(τ)+(N-1)(N-3)/4τ^2 )u(τ)+λu(τ)=f(τ,τ(1-N)/2 u)u(τ),τ〉0, u∈H, N≥3. (P),where f ∈ C((0,+∞) ×R,R), f(τ,s) goes to p(τ) and q(τ) uniformly in τ 〉 0 as s→ 0 and s→+∞ respectively, 0≤ p(τ) ≤ q(τ) ∈L^∞(0,∞). Moreover, for τ 〉 0, f(τ, s) is nondecreasing in s≥ 0. Some existence and non-existence of positive solutions to problem (P) are proved without assuming that p(τ) = 0 and q(τ) has a limit at infinity. Based on these results, we get the existence of positive solutions for an elliptic problem.
基金
the National Natural Science Foundation of China(No.10571174,No.10631030)
CAS:KJCX3SYW-S03