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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:
[1] Bebernes J., Adv. Differential Equations 2 (6) pp 927– (1997)
[2] DOI: 10.1002/cpa.3160380105 · Zbl 0581.35021
[3] Przeradzki B., Colloq. Math. 92 pp 141– (2002) · Zbl 0992.35037
[4] Stańczy R., Nonlinear Anal. 47 pp 3579– (2001) · Zbl 1042.35548
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