Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, a...We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, and the resolution of singularities. As an application, we construct a new algebraic surface which is the quotient of ball.展开更多
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075109)
文摘Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
基金supported by National Natural Science Foundation of China (Grant No.10731030)the Innovation Program of Shanghai Municipal Education Commission (Grant No. 11ZZ18)
文摘We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, and the resolution of singularities. As an application, we construct a new algebraic surface which is the quotient of ball.
