In this paper we study the solvability of boundary value problems in a bounded cylindrical domain of variables (x, t) for composite type differential equations
Dt((−1)p+1Dt2pu−Δu)+μu = f(x,t),Dt2((−1)p+1Dt2pu−Δu)+μu = f(x,t)
(⁠Dtk = ∂k∂tk, Dt = Dt1, Δ is a Laplace operator with respect to the space variables, p > 1 is a natural number) and some of their generalizations. The existence and uniqueness theorems for regular solutions (all the derivatives of equation are the Sobolev generalized derivatives) are proved.
Topics
Operator theory, Partial differential equations
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