Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable

作者：Zhong, Qiuyan; Zhang, Xingqiu^*

来源：Boundary Value Problems, 2017, 2017(1): 90.

DOI：10.1186/s13661-017-0822-9

• integral boundary value
• cone
• two positive solutions
• singularity

This article deals with integral boundary value problems of the second-order differential equations @@@ {u ''(t) + a(t)u'(t) + b(t)u(t) + f(t,u(t)) = 0, t is an element of J(+), @@@ u(0) = integral(1)(0) g(s)u(s)ds, u(1) = integral(1)(0) h(s)u(s)ds, @@@ where a is an element of C(J), b is an element of C(J, R-), f is an element of C(J(+) x R+, R+) and g, h is an element of L-1(J) are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity f permits the singularity on the space variable.

• 出版日期2017-6-17
• 单位聊城大学; 济宁医学院