Existence of triple positive solutions for second order boundary value problems with one-dimensional \(p\)-Laplacian (Q2906315)

The paper deals with the equation NEWLINE\[NEWLINE(\varphi_p(x'(t))'+\phi(t)f(t,x(t),x'(t))=0,\quad 0<t<1NEWLINE\]NEWLINE associated with the pair of the boundary conditions NEWLINE\[NEWLINEx'(0)=0, \enskip x(1)=\sum_{i=1}^{m-2}\alpha_ix(\xi_i)NEWLINE\]NEWLINE and NEWLINE\[NEWLINEx'(1)=0, \enskip x(0)=\sum_{i=1}^{m-2}\alpha_ix(\xi_i),NEWLINE\]NEWLINE where \(\varphi_p(s)=|s|^{p-2}s\), \(p>1\), \(0<\xi_1<\xi_2<\dotsb<\xi_{m-2}<1\), \(\alpha_i\geq 0\), with \(0<\sum_{i=1}^{m-2}\alpha_i<1\), \(m\geq 3\). The author gives sufficient conditions in order to be able to apply a generalization of the Leggett-Williams fixed point theorem due to Avery and Peterson on cones in Banach spaces to show the existence of triple positive solutions of the problem.