Bounds for the solution of the Poisson-Boltzmann equation about a cylindrical particle (Q1060341)

Using maximum principle techniques, the authors construct pointwise upper and lower bounds for the solution of the boundary value problem \[ (1/r)(d/dt)(r du/dr)=-\sinh u,\quad 0<r_ 0<r,\quad u(r_ 0)=u_ 0>0,\quad \lim_{r\to \infty}u=0. \]