Existence and multiplicity results for a class of generalized one-dimensional \(p\)-Laplacian problem (Q1049035)

The authors study the boundary value problem \[ \begin{aligned} &(\varphi_p(u'))'+\phi(t)f(t,u(t),u'(t))=0,\quad 0<t<1,\\ &au(0)-bu'(0)=\sum^{m-2}_{i=1}a_iu(\xi_i),\;cu(1)+du'(1)=\sum^{m-2}_{i=1}b_iu(\xi_i), \end{aligned} \] where \(\varphi_p(u)\) is the \(p\)-Laplacian operator. Some results are obtained for the existence of at least three positive solutions by using fixed point theory. The interesting point is the nonlinear term \(f\) which involves the first order derivative explicitly.