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...Tokyo j math vol no on the generalized thomas fermi di erential equations and applicability of saito s transformation ichiro tsukamoto communicated by m maejima dedicated to professor junji kato his sixtieth birthday introduction let us consider equation x prime p t alpha d dt geqq where is a nonzero real constant denotes nonnegative valued branch in papers succeeded investigating asymptotic behavior solutions lambda positive with aid y psi phi z ty which transforms rst order algebraic frac dz dy yz particular solution an arbitrary moreover we considered case pme lambdat using form similar such as pm e this also since coe cients two transformations above er more general theta received july revised june are su ciently smooth functions call purpose ofthis paper determine that can transform determining will be suitably chosen achieved from conclusion ofthat section shall nd four beta whose importance stated have speci ed so satisfy our therefore treated same way while already dealt other ...