Multiple positive solutions for some multi-point boundary value problems with p-Laplacian

作者：Guo Yanping; Ji Yude^*; Liu Xiujun

来源：Journal of Computational and Applied Mathematics, 2008, 216(1): 144-156.

DOI：10.1016/j.cam.2007.04.023

• multiple positive solutions
• the five functionals fixed point theorem
• p-Laplacian

This paper deals with the existence of multiple positive solutions for the quasilinear second-order differential equation
(Phi(p) (u'(t)))' + a (t)f (t, u (t)) = 0, t is an element of (0, 1),
subject to one of the following boundary conditions:
(phi(p) (u' (0)) = (m-2)Sigma(i=1)a(i)phi(p)(u'(xi(i))), u(1) = (m-2)Sigma(i=1)b(i)u(xi(i)),
or
u(0) = (m-2)Sigma(i=1)a(i)(u'(xi(i)), phi(p)(u'(1)) = (m-2)Sigma(i=1)b(i)phi(p)(u'(xi(i))),
where phi(p)(s)=|S|(p-2)s, p > 1, 0< xi(1) < xi(2) <... <xi(m-2) < 1,andai, b(i) satisfy a(i), b(i) is an element of [0, infinity),(i=1, 2,..., m-2),0 < (m-2)Sigma(i=1)a(i) < 1,0<(m-2)Sigma(i=1)b(i) < 1. Using the five functionals fixed point theorem, we provide sufficient conditions for the existence of multiple (at least three) positive solutions for the above boundary value problems.

• 出版日期2008-6-15
• 单位河北大学