Global structure of positive solutions for third-order semipositone integral boundary value problems

Abstract

<abstract><p>In this paper, we were concerned with the global behavior of positive solutions for third-order semipositone problems with an integral boundary condition</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{split} &amp;y'''+\beta y''+\alpha y'+\lambda f(t,y) = 0,\; \; \; t\in(0,1),\\ &amp;y(0) = y'(0) = 0,\; \; \; y(1) = \chi\int^1_0y(s)ds, \end{split} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ \alpha\in(0, \infty) $ and $ \beta\in(-\infty, \infty) $ are two constants, $ \lambda, \chi $ are two positive parameters, and $ f\in C([0, 1]\times[0, \infty), \mathbb{R}) $ with $ f(t, 0) &lt; 0 $. Our analysis mainly relied on the bifurcation theory.</p></abstract>