Positive solutions for singular impulsive Dirichlet boundary value problems (Q1741786)

The authors present sufficient conditions for the existence of one or two positive classical solutions for the following singular Dirichlet boundary value problem \[ \begin{gathered} -u''(t)-\frac{1}{u^\alpha(t)}= \lambda f (t, u(t)), \quad t \in \Omega,\\ u'(t_i^+)-u'(t^-_i)=I_i(u(t_i)), \quad i=1,\dots, p,\\ u(0)=u(1)=0 \end{gathered} \] where \(\lambda \in (0,+\infty)\), \(\alpha \in (0,1)\), \(\Omega = (0,1)\setminus \{t_1,\dots, t_p\}\), \(0=t_0<t_1< \dots < t_p < t_{p+1}=1\), \(f\in C([0,1]\times [0,+\infty);[0,+\infty))\) and \(I_i \in C([0,\infty);(-\infty,0])\) for each \(i=1,\dots,p\). The results are obtained by using a variational method and critical point theory.