On p(x)-Kirchhoff-type equation involving p(x)-biharmonic operator via genus theory - Taarabti, S.; El Allali , Z.; Ben Haddouch, K. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 517.9 The paper deals with the existence and multiplicity of nontrivial weak solutions for the p(x)-Kirchhoff-type problem -M\!(_Ω1p(x)|Δ u|^p(x) dx)\!Δ_p(x)^2 u = f(x,u)inΩ, u = Δ u = 0onΩ. By using variational approach and Krasnoselskii’s genus theory, we prove the existence and multiplicity of solutions for the p(x)-Kirchhoff-type equation.