摘要
设f:[0,1]×R2→R满足Caratheodory条件(1-t)e(t)∈L1(0,1),∫01a(t)tdt≠1,a(t)t∈L1[0,1].运用Leray-Schauder原理考虑二阶奇异边值问题x″(t)=f(t,x(t),x′(t))+e(t),0<t<1;x(0)=0,x(1)=∫01a(t)x(t)dt在C1[0,1)上解的存在性.
Let f:[0,1]×R2→Rbe a function meeting Caratheodory's conditions, (1-t)e(t)∈L^1 (0, 1), and ∫0^1a(t)tdt≠1,a(t)t∈L1[0,1]. The existence of solutions to the singular second-order boundary-value floa(t)x(t)dt on problemx″(t)=f(t,x(t),x′(t))+e(t),0〈t〈1;x(0)=0,x(1)= ∫0^1a(t)x(t)dt on C^1[0,1] was taken into consideration by using Leray-Schauder principle.
出处
《兰州理工大学学报》
CAS
北大核心
2007年第2期137-140,共4页
Journal of Lanzhou University of Technology