Global behavior of positive solutions for some semipositone fourth-order problems

Abstract

Abstract In this paper, we study the global behavior of positive solutions of fourth-order boundary value problems {u′′′′=λf(x,u),x∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0, $$ \textstyle\begin{cases} u''''=\lambda f(x,u), \quad x\in (0,1), \\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} $$ where f:[0,1]×R+→R $f: [0,1]\times \mathbb{R^{+}} \to \mathbb{R}$ is a continuous function with f(x,0)0 $\lambda >0$. The proof of our main results are based upon bifurcation techniques.

Keywords

• 34B18
• 34B16
• 34B25
• 47H11