Solvability of the Vallée-Poussin nonlinear boundary-value problems

We consider the solvability of a boundary-value problem of form (1), (2) in the class of nonlinearities of f, for which the traditional restrictions of the Lifschitz-conditions type are replaced by concavity (or generalized concavity) conditions with respect to specially chosen variables.Senior Lecturer.Candidate of Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 700–703, May, 1992.