Nontrivial solutions of m-point boundary value problems for singular second-order differential equations with a sign-changing nonlinear term

Authors:
Lishan Liu;Bingmei Liu;Yonghong Wu
Affiliations:
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People's Republic of China and Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA ...;School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People's Republic of China;Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
Cited 1

Positive solutions of a nonlinear three-point boundary value problem

Applied Mathematics and Computation
Multiple rositive solutions for a three-point boundary value problem

Mathematical and Computer Modelling: An International Journal

Existence of Positive Solutions for Multi-Point Boundary Value Problem with Strong Singularity

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper concerns the existence of nontrivial solutions for the following singular m-point boundary value problem with a sign-changing nonlinear term {(Lu)(t)+h(t)f(t,u)=0,0(-~,+~) is a sign-changing continuous function and may be unbounded from below. By applying the topological degree of a completely continuous field and the first eigenvalue and its corresponding eigenfunction of a special linear operator, some new results on the existence of nontrivial solutions for the above singular m-point boundary value problem are obtained. An example is then given to demonstrate the application of the main results. The work improves and generalizes the main results of [G. Han, Y. Wu, Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms, J. Math. Anal. Appl. 325 (2007) 1327-1338; J. Sun, G. Zhang, Nontrivial solutions of singular superlinear Sturm-Liouville problem, J. Math. Anal. Appl. 313 (2006) 518-536].