Existence results for damped regular equations under periodic or Neumann boundary conditions
In this article, the authors state a version of the averaging and a method to construct lower and upper solutions in the reversed order that are suitable for both the periodic and the Neumann boundary conditions. As an application, they study the damped regular differential equation \[ \ddot{x}+c\dot{x}=\nu g(t)x^\lambda-h(t)x^\mu,\tag{1} \] where \(\lambda,\mu>0,\) \(g,h\in C([0,T]),\) \(c\in\mathbb{R}\) and \(\nu\) is a parameter. Indeed, under periodic conditions, that is \[ x(0)=x(T),\quad \dot{x}(0)=\dot{x}(T), \] or Neumann boundary conditions, i.e., \[ \dot{x}(0)=\dot{x}(T)=0, \] the existence of positive solutions of the equation (1) is investigated.
scientific article; zbMATH DE number 7472997
scientific article