Abstract: By using the theory of variable exponent Sobolev spaces and the Clark’s theorem in critical point theory, the author investigated Navier boundary value problem for a class of Kirchhofftype p(x)-biharmonic equation. When the nonlinear term satisfied the critical condition and growed linearly near zero, the author obtained the existence of infinitely many solutions.

Key words: critical point, p(x)-biharmonic equation, Navier boundary value problem