Multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one-dimensional p-Laplacian

作者：Feng Hanying^*; Pang Huihui; ge Weigao

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 69(9): 3050-3059.

DOI：10.1016/j.na.2007.08.075

• Multipoint boundary value problem
• Fixed point theorem
• Symmetric positive solution
• One-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for the one-dimensional p-Laplacian
(phi(p)(u'(t)))' + q(t) f (t, u(t),u'(t)) = 0. t epsilon (0,1).
subject to the boundary conditions
u(0) = Sigma(n)(i=1) mu(i)u(xi(i)). u(1) = Sigma(n)(i=1) mu(i)u(eta(i)).
where phi(p)(s) = vertical bar s vertical bar(p-2)s.p > 1.mu(i) >= 0.0 <= Sigma(n)(i=1) mu(i) < 1.0 < xi(1) < xi(2) < . . . < xi(n) < 1/2. xi(i) + eta(i) = 1.i = 1.2,....n. Applying a fixed point theorem of functional type in a cone, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f contains the first-order derivative explicitly.

• 出版日期2008-11-1
• 单位北京理工大学