摘要：In this paper, we investigate the existence of a reversed S-shaped component in the positive solutions set of the fourth-order boundary value problem { u ′′′′ ( x ) = λ h ( x ) f ( u ( x ) ) , x ∈ ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , $$\textstyle\begin{cases} u''''(x)=\lambda h(x)f(u(x)),\quad x\in(0,1),\\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} $$ where λ > 0 $\lambda>0$ is a parameter, h ∈ C [ 0 , 1 ] $h\in C[0,1]$ and f ∈ C [ 0 , ∞ ) $f\in C[0,\infty )$ , f ( 0 ) = 0 $f(0)=0$ , f ( s ) > 0 $f(s)>0$ for all s > 0 $s>0$ . By figuring the shape of unbounded continua of solutions, we show the existence and multiplicity of positive solutions with respect to parameter λ, and especially, we obtain the existence of three distinct positive solutions for λ being in a certain interval.
关键词：boundary value problem ; positive solutions ; principal eigenvalue ; bifurcation
