Positive solutions for elastic beam equations with nonlinear boundary conditions and a parameter
Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, P.R. China
Boundary Value Problems 2014, 2014:80 doi:10.1186/1687-2770-2014-80Published: 9 April 2014
This paper is concerned with the existence, nonexistence, and uniqueness of convex monotone positive solutions of elastic beam equations with a parameter λ. The boundary conditions mean that the beam is fixed at one end and attached to a bearing device or freed at the other end. By using fixed point theorem of cone expansion, we show that there exists such that the beam equation has at least two, one, and no positive solutions for , and , respectively; furthermore, by using cone theory we establish some uniqueness criteria for positive solutions for the beam and show that such solution depends continuously on the parameter λ. In particular, we give an estimate for critical value of parameter λ.
MSC: 34B18, 34B15.