The existence of positive solutions for the singular two-point boundary value problem - Niu, Yanmin; Yan, Baoqiang (Topological Methods in Nonlinear Analysis, 2017)
In this paper, we consider the following boundary value problem: $$ \begin{cases} ((-u'(t))^n)'=nt^{n-1}f(u(t)) &\text{for }0< t< 1,\\ u'(0)=0,\quad u(1)=0, \end{cases} $$% where $n> 1$. Using the fixed point theory on a cone and approximation technique, we obtain the existence of positive solutions in which $f$ may be singular at $u=0$ or $f$ may be sign-changing.