Boundary value problems arising in the percolation of water from a cylindrical reservoir into the surrounding soil (Q2572120)

The existence of solutions to a general class of second-order boundary value problems is studied. The authors use the nonlinear alternative of the Leray-Schauder type to establish the existence of a solution to the problem \[ ((G(y))'+p(t)y^m )'+q(t)f(t,y) =p'(t)y^m,\;0<t<1,\quad y(0)=0,\;\;y(1)=b_0>0. \] For particular \(G\), \(m\), \(p\), \(q\), \(f\) and \(b_0\), the above problem arises from the Boussinesq equation describing the percolation of water from a cylindrical reservoir into the surrounding soil.