Multiple Positive Solutions for a Fourth-order Boundary Value Problem - doi: 10.5269/bspm.v21i1-2.7503

Yaoliang Zhu; Peixuan Weng

doi:10.5269/bspm.v21i1-2.7503

Multiple Positive Solutions for a Fourth-order Boundary Value Problem - doi: 10.5269/bspm.v21i1-2.7503

Authors

Yaoliang Zhu Nanjing University of Technology
Peixuan Weng South China Normal University

DOI:

https://doi.org/10.5269/bspm.v21i1-2.7503

Keywords:

Multiple Positive Solutions, Fourth-order Boundary Value Problem

Abstract

In this paper, we discuss the existence of multiple positive solutions
for the fourth-order boundary value problem
u^{(4)}(t) = f(t, u(t), u''(t)), 0 < t < 1,
u(0) = u(1) = u''(0) = u''(1) = 0,
where f : [0, 1] × [0,1) \rightarrow [0,1) is continuous. Existence theorems are established via the theory of fixed point index in cones.