Existence and multiplicity results for a newp(x)-Kirchhoff problem

By Mohamed Karim Hamdani, A. Harrabi, F. Mtiri, Dušan D. Repovš. Nonlinear Analysis, 2019

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Abstract In this work, we study the existence and multiplicity results for the following nonlocal p ( x ) -Kirchhoff problem: (0.1) − a − b ∫ Ω 1 p ( x ) | ∇ u | p ( x ) d x d i v ( | ∇ u | p ( x ) − 2 ∇ u ) = λ | u | p ( x ) − 2 u + g ( x , u )  in  Ω , u = 0 ,  on  ∂ Ω , where a ≥ b > 0 are constants, Ω ⊂ R N is a bounded smooth domain, p ∈ C ( Ω ¯ ) with N > p ( x ) > 1 , λ is a real parameter and g is a continuous function. The analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties.

Subfields: Applied Mathematics, Mathematical Physics

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