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On the boundary value problem for the elliptic functional-differential equation with contractions. (English) Zbl 1054.35117
The paper deals with the following boundary value problem for elliptic functional differential equations \[ -\Delta (\sum_{k=0}^l a_k u(q^{-k}x)) = f(x), \quad x \in Q, \] \[ u(x) = 0, \quad x \in \partial Q, \] considered in the weighted spaces \(H_{2,s}^k(Q)\). The author shows that the above problem is always Fredholm in \(H_{2,s}^k(Q)\) with suitable exponents \(k\) and \(s\).

MSC:
35R10 Functional partial differential equations
35J15 Second-order elliptic equations
47N20 Applications of operator theory to differential and integral equations
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