Applications of Mathematics

, Volume 58, Issue 1, pp 93–110

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

Article

DOI: 10.1007/s10492-013-0004-8

Cite this article as:
Yao, Q. Appl Math (2013) 58: 93. doi:10.1007/s10492-013-0004-8

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.

Keywords

nonlinear ordinary differential equation singular nonlinearity positive solution eigenvalue interval 

MSC 2010

34B15 34B16 34B18 

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsNanjing University of Finance and EconomicsNanjingPeople’s Republic of China

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