On Unique Solvability of a Nonlocal Boundary-value Problem for a Loaded Multidimensional Chaplygin's Equation in the Sobolev Space

Boundary-value problems for loaded equations in the plane in the case of loaded parts consist of traces of an unknown solution or its first normal derivatives, are well studied. The multidimensional loaded differential equations are relatively less investigated. Moveover, when the loaded part consists of not only the traces of the solution or its first normal derivatives, but also second derivatives of the solutions, the classical methods are not effective. Therefore, in this paper, we propose a method which overcomes these difficulties. Under some conditions on coefficients of the loaded multidimensional Chaplygin's equation, we prove existence and uniqueness of a solution of a nonlocal boundary-value problem in the Sobolev space W-2(3)(Q).