Solution curves of 2m-th order boundary-value problems

Electronic Journal of Differential Equations

卷:2004

关键词: Ordinary differential equations;    nonlinear boundary value problems.;   

DOI  :  

来源: DOAJ

【 摘 要 】

We consider a boundary-value problem of the form $L u = lambda f(u)$, where $L$ is a $2m$-th order disconjugate ordinary differential operator ($m ge 2$ is an integer), $lambda in [0,infty)$, and the function $f : mathbb{R} o mathbb{R}$ is $C^2$ and satisfies $f(xi) > 0$, $xi in mathbb{R}$. Under various convexity or concavity type assumptions on $f$ we show that this problem has a smooth curve, $mathcal{S}_0$, of solutions $(lambda,u)$, emanating from $(lambda,u) = (0,0)$, and we describe the shape and asymptotes of $mathcal{S}_0$. All the solutions on $mathcal{S}_0$ are positive and all solutions for which $u$ is stable lie on $mathcal{S}_0$.

【 授权许可】

Unknown