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On integral nonlocal boundary value problems for some partial differential equations. (English) Zbl 1227.35015
Summary: The present paper deals with the results of investigation of nonclassical problems for elliptic and hyperbolic partial differential equations with integral nonlocal boundary conditions. Boundary value problems for elliptic equations on multidimensional cylindrical domains with one and two integral boundary conditions are considered. The nonclassical problems for elliptic equation are investigated applying a variational approach in suitable Sobolev spaces and existence and uniqueness results are proved. Nonclassical problems for multidimensional hyperbolic equation with integral boundary conditions are studied and the uniqueness of the classical solution is proved.

35A15 Variational methods applied to PDEs
35R09 Integro-partial differential equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35J25 Boundary value problems for second-order elliptic equations