A degenerate Kirchhoff-type problem involving variable s(<middle dot>)-order fractional p(<middle dot>)-Laplacian with weights

This paper deals with a class of nonlocal variable s(.)-order fractional p(.)-Kirchhoff type equations: { K(integral(2N )(R)1/p(x,y) |phi(x)-phi(y)|(p(x,y))/|x-y|(N+s(x,y)p(x,y) )dx dy)(-Delta)(s(<middle dot>))(p(<middle dot>))phi(x) = f(x,phi) in Omega, phi=0 on R-N\Omega.Under some suitable conditions on the functions p, s, K and f , the existence and multiplicity of nontrivial solutions for the above problem are obtained. Our results cover the degenerate case in the p(<middle dot>) fractional setting.