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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
##### Keywords:
weighted spaces; Fredholm property