Existence and multiplicity of solutions for fractional p(x, .)-Kirchhoff-type problems in ℝN. Issue 9 (4th July 2021) - Azroul, E.; Benkirane, A.; Shimi, M.
Abstract : The purpose of this paper is to investigate the existence and multiplicity of solutions for the following class of fractional p ( x, . ) -Kirchhoff-type problems in R N 1 ( P M s ) M ∫ R N × R N 1 p ( x, y ) | u ( x ) − u ( y ) | p ( x, y ) | x − y | N + s p ( x, y )   d x d y − Δ p ( x, . ) s u ( x ) + | u | p ¯ ( x ) − 2 u = f ( x, u ) i n   R N, u ∈ W s, p ( x, y ) ( R N ) . We first establish the compact embedding of the space W s, p ( x, y ) ( R N ) into L w ( x ) q ( x ) ( R N ) . Using this embedding result and some critical-points theorems, we obtain the existence and multiplicity results.