Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503066 | Journal of Mathematical Analysis and Applications | 2005 | 14 Pages |
Abstract
This paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth-order beam equation u(4)(t)+ηuâ³(t)âζu(t)=λf(t,u(t)), 00Ë such that the above boundary value problem (BVP) has at least two, one and no positive solutions for 0<λ<λ*, λ=λ* and λ>λ*, respectively. Furthermore, by using the semiorder method on cones of Banach space, we establish a uniqueness criterion for positive solution of the BVP. In particular such a positive solution uλ(t) of the BVP depends continuously on the parameter λ, i.e., uλ(t) is nondecreasing in λ, limλâ0+âuλ(t)â=0 and limλâ+ââuλ(t)â=+â for any tâ[0,1].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xi-Lan Liu, Wan-Tong Li,