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） go...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.展开更多
基金the National Natural Science Foundation of China(No.10571174,No.10631030)CAS:KJCX3SYW-S03
文摘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.
