Refined approximations of the solutions of a coupled system with turning points
The authors present the asymptotic behavior of solutions of the following boundary value problem \[ u''=v,\quad \epsilon v''+f(u,u')v'- q(x,u,u')v=0,\quad x\in I, \] \[ u(0,\epsilon)=u(1,\epsilon)=0,\quad v(0,\epsilon)=v_ 0,\quad v(1,\epsilon)=v_ 1, \] where \(g(x,u,u')\geq 0\), \(f(u,u')\) has turning points on I, and \(\epsilon\) is a small parameter. They provide upper and lower solutions, \(\beta\) (x,\(\epsilon\)) and \(\alpha\) (x,\(\epsilon\)), exhibiting boundary layer and interior layer behavior, for which \(\lim_{\epsilon \to 0+}(\beta (x,\epsilon)-\alpha (x,\epsilon))=0,\) uniformly on I.
scientific article; zbMATH DE number 4210574
scientific article