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On a boundary value problem for a nonlocal elliptic equation. (English) Zbl 1071.35047
Authors’ abstract: The existence of a positive radial solution to the Dirichlet boundary value problem for the second-order elliptic equation $-\Delta u= f\Biggl(u,\int_U u\Biggr),$ where $$U= B(0, R)\setminus\overline B(0,\rho)$$, with weak assumptions on the nonlinear term $$f$$, is proved. The method based on the Krasnosel’skii fixed point theorem enables to find many solutions to the problem. Solutions for the same problem but with $$U= B(0, R)$$ and with nonlinear term $$f$$ depending explicitely on $$I\times I$$ are found as well.

##### MSC:
 35J60 Nonlinear elliptic equations 47J25 Iterative procedures involving nonlinear operators
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##### References:
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