The Symmetric Positive Solutions of Four-Point Problems for Nonlinear Boundary Value Second-Order Differential Equations

Recently, there are many results about the existence and multiplicity of positive solutions for nonlinear second-order differential equations(see[7],[5],[3]). Henderson and Thompson(see[4]), Li and Zhang (see[2]) studied the multiple symmetric positive and nonnegative solutions of second-order ordinary differential equations. Yao (see[6]) considered the existence and iteration of n symmetric positive solutions for a singular two-point boundary value problem(BVP). Sun(see[8]) considered the existence and multiplicity of symmetric positive solutions for three-point boundary value problem. Inspired by the works mentioned above, in this paper, we study the existence of symmetric positive solutions of second-order four-point differential equations as follows, { −u′′(t) = f(t, v), −v′′(t) = g(t, u), 0 ≤ t ≤ 1, (1)