Positive solutions of singular Sturm-Liouville boundary value problems (Q2756184)

The authors study the Sturm-Liouville boundary value problem consisting of the equation NEWLINE\[NEWLINE(p(t)u'(t))'+\lambda a(t)f(t, u(t))=0, \qquad 0<t<1, \tag{1}NEWLINE\]NEWLINE with the boundary conditions NEWLINE\[NEWLINE\alpha u(0)-\beta p(0)u'(0)=0,\qquad \gamma u(1)+\delta p(1)u'(1)=0,NEWLINE\]NEWLINE with \(\lambda >0\) and \(a\) is allowed to be singular at both end points \(t=0\) and \(t=1\). The authors use a fixed-point theorem in cone (due to Krasnosel'skij) to prove the existence of positive solutions.