On a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type
نویسنده
چکیده
We study the existence of positive solutions to the following nonlocal boundary value problem −K ‖u‖2 Δu λus−1 f x, u inΩ, u 0 on ∂Ω, where s ∈ 1, 2 , f : Ω×R → R is a Carathéodory function,K : R → R is a positive continuous function, and λ is a real parameter. Direct variational methods are used. In particular, the proof of the main result is based on a property of the infimum on certain spheres of the energy functional associated to problem −K ‖u‖2 Δu λus−1 in Ω, u|∂Ω 0.
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تاریخ انتشار 2010