具有共振的边值问题解的存在性

The Existence of Solutions for Boundary Value Problem at Resonance

利用Mawhin的重合度理论,研究具有共振的n-阶m-点边值问题x^((n))(t)=f(t,x(t),x′(t),…,x^((n-1))(t)),t∈(0,1)x(0)=x(η),x′(0)=x″(0)=…=x^((n-2))(0)=0,x^((n-1))(1)=α_ix^((n-1))(ξ_i)解的存在性,其中n≥2,m≥3,f:[0,1]×R^n→R将有界集映为有界集,且当x(t)∈C^(n-1)[0,1]时,f(t,x(t),x′(t),…,x^((n-1))(t))∈L^1[0,1],0<ξ_1<ξ_2<…<ξ_(m-2)<1,0<η<1,α_i∈R.在这里并不要求f具有连续性.

Using the coincidence degree theory due to Mawhin,we study the existence ofsolutions for n-order m-point boundary value problemwhere n≥2,m≥3,f：[0,1]×Rn→R mapping bounded set to bounded set,f（t,x（t）,x＇（t）,…,x（（n-1））（t））∈L1[0,1]forx（t）∈C（n-1）[0,1],0ξ1ξ2…ξ（m-2）1,0η1,α_i∈R.We don＇t need that f is continuous.