This work inaugurates a
new and
general solution method for
arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind
order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need
not satisfy any kind of monotonicity properties. Moreover, the solution method is completely
type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the
continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any
discontinuous and
measurable function.
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