A detailed numerical analysis of the boundary value problem resulting from the most general Skyrme type lagrangian containing up to quartic terms in field gradients is presented. The additional parameters in the lagrangian can be related to pion-pion scattering lengths. It is found that solutions to the boundary value problem does not exist for all values of the parameters and in particular, for the values predicted from pion-pion scattering data. Physical quantities of the nucleon are calculated for the highest possible values of the parameters admitting a solution and are compared with the corresponding values for the Skyrme model and experimental values.