Multiple solutions for a class of p(x)-Kirchhoff type problems with Neumann boundary conditions

Nontrivial Solutions for a Class ofp-Kirchhoff Dirichlet Problem

“…Kirchhoff-type problem setting on a bounded domain also attracts a lot of attention, see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the references therein. For example, we refer to some recent works [8,9] in which some interesting results on the problems with Dirichlet or Neumann boundary conditions have been obtained. Chung [10] studied Kirchhoff type problems with Robin boundary conditions and indefinite weights.…”

Solutions for the P(x)-Laplacian With Dependence on the Gradient

“…Problems with variable exponent growth conditions also appear in the modelling of stationary thermo-rheological viscous flows of non-Newtonian fluids and in the mathematical description of the processes filtration of an ideal barotropic gas through a porous medium. The detailed application backgrounds of the p(x)-Laplacian can be found in [3,6,22,25] and references therein.…”

On the Frictional Contact Problem of p(x)-Kirchhoff Type

“…where Ω ⊆ R 2 is a bounded domain with smooth enough boundary Γ, partitioned in three parts Γ 1 , Γ 2 , Γ 3 such that meas (Γ i ) > 0, (i = 1, 2, 3); The study of the p(x)-Kirchhoff type equations with nonlinear boundary conditions of different class have attracted expensive attention in recent years, we refer to some interesting works [1,6,13,16] and references therein. One reason of such interest is that various real fields require PDE problems with variable exponent, for example, electrorheological fluids and image restoration.…”