An upper and lower solution theory for singular Emden-Fowler equations
Results guaranteeing the existence of positive solutions to the Dirichlet boundary value problem \[ y''+ q(t) f(t,q)= 0,\quad 0< t< 1,\quad y(0)= 0= y(1),\tag{\(*\)} \] are obtained. Here, \(f: [0,1]\times (0,\infty)\to \mathbb{R}\) is continuous and may be singular at \(y= 0\), \(q\in C(0,1)\), \(q> 0\) on \((0,1)\) and \(\int^1_0 x(1- x)q(x) dx< \infty\). The upper and lower solutions technique is used. Similar results can be established if Sturm-Liouville boundary conditions are considered in \((*)\).
scientific article; zbMATH DE number 1788074
scientific article