Abstract

In this article, we first give the representation of solutions for the oblique derivative boundary value problem of generalized Lavrent$'$ev-Bitsadze equations including the Lavrent$'$ev-Bitsadze equation. Next we verify the uniqueness of solutions of the above problem. Finally we prove the solvability of oblique derivative problems for quasilinear mixed (generalized Lavrent$'$ev-Bitsadze) equations of second order, at the same time the estimates of solutions of the above problem is also obtained. The above problem is an open problem proposed by J. M. Rassias.

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