, Volume 58, Issue 1, pp 93-110
Date: 21 Feb 2013

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

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Abstract

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.

This work was supported by the National Natural Science Foundation of China (11071109).