关键词: Kirchhoff型方程, p(x)-Laplace算子, 局部环绕, 非平凡解, 临界点

Abstract: By using the local linking theorem in critical point theory and the theory of variable exponent Sobolev space, the author proved the existence of nontrivial solutions for Kirchhoff-type equation with p(x)-Laplacian operator without  assuming  the  (AR) type superlinearity condition held.

Key words: Kirchhoff-type equation, p(x)-Laplacian operator,  , local linking, nontrivial solution, critical point