科研之友
微信
新浪微博
Facebook
分享链接
摘要
The existence of at least three positive solutions for differential equation (phi(p)(u'(t)))' + g(t)f(t, u(t), u'(t)) = 0, under one of the following boundary conditions: u(0) = Sigma(m-2)(i=1)a(i)u(xi(i)), phi(p)(u'(1)) = Sigma(m-2)(i=1) b(i)phi(p)(u'(xi(i))) or phi(p)(u'(0)) = Sigma(m-2)(i=1) a(i)phi(p)(u'(xi(i))), u(1) = Sigma(m-2)(i=1) b(i)u(xi(i)) is obtained by using the H. Amann fixed point theorem, where phi(p)(s) = vertical bar s vertical bar(p-2) s, p > 1, 0 <xi(1) < xi(2) < . . . < xi(m-2) < 1, a(i) > Sigma(m-2)(i=1)a(i) < 1, 0 < Sigma(m-2)(i=1) b(i) < 1. The interesting thing is that g(t) may be singular at any point of [0,1] and f may be noncontinuous.
