Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem

摘要

We consider the classical nonlinear fourth-order two-point boundary value problem . In this problem, the nonlinear term h(t)f(t, u(t), u′(t), u″(t)) contains the first and second derivatives of the unknown function, and the function h(t)f(t, x, y, z) may be singular at t = 0, t = 1 and at x = 0, y = 0, z = 0. By introducing suitable height functions and applying the fixed point theorem on the cone, we establish several local existence theorems on positive solutions and obtain the corresponding eigenvalue intervals. Keywords nonlinear ordinary differential equation singular nonlinearity positive solution eigenvalue interval MSC 2010 34B15 34B16 34B18 This work was supported by the National Natural Science Foundation of China (11071109).