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On an elliptic Kirchhoff-type problem depending on two parameters. (English) Zbl 1192.49007

Summary: On a bounded domain Ω n , we consider a non-local problem of the type

-K Ω |u(x)| 2 dxΔu=λf(x,u)+μg(x,u)inΩ,u=0onΩ·

Under rather general assumptions on K and f, we prove, in particular, that there exists λ * >0 such that, for each λ>λ * and each Carathéodory function g with a sub-critical growth, the above problem has at least three weak solutions for every μ0 small enough.

MSC:
49J20Optimal control problems with PDE (existence)
35J20Second order elliptic equations, variational methods
References:
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