Name
Title | ||
|---|---|---|
Positive solutions of fourth-order multi-point boundary value problems with bending term |
Abstract | ||
|---|---|---|
In this paper, we study m-point boundary value problem for fourth-order ordinary differential equation with bending term x″x(4)(t)=g(t)f(t,x(t),x″(t)),t∈(0,1),x(0)=0,x(1)=∑i=1m-2aix(ξi),x″(0)=0,x″(1)=∑i=1m-2bix″(ξi),where 0=ξ0<ξ1<ξ2<⋯<ξm-2<ξm-1=1. By constructing an available integral operator and combining fixed point index theorem, we establish sufficient conditions for the existence of positive solutions under some conditions concerning the first eigenvalue corresponding to the relevant linear operator. The interesting point of the results is that the nonlinear term g may be singular at t=0 and (or) t=1, moreover f(t,u,v) is also allowed to have singularity at u=0 and (or) v=0. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.amc.2007.04.028 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Multi-point boundary value problems,Positive solutions,Fixed point index theorem,Cone | Boundary value problem,Differential equation,Fixed-point index,Ordinary differential equation,Mathematical analysis,Singularity,Linear map,Eigenvalues and eigenvectors,Mathematics,Fixed-point theorem | Journal |
Volume | Issue | ISSN |
194 | 2 | 0096-3003 |
Citations | PageRank | References |
8 | 1.11 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xinguang Zhang | 1 | 163 | 23.65 |
| Lishan Liu | 2 | 188 | 35.41 |