Infinitely Many Solutions for a Fourth-Order Semilinear Elliptic Equations Perturbed from Symmetry

In this paper, we study the existence of multiple solutions for the following biharmonic problem

Δ²u = f(x, u) + g(x, u) in Ω,

    u = Δu = 0 on ∂Ω,

where Ω ⊂ ,(N > 4) is a smooth bounded domain and f(x, ξ) is odd in ξ, g(x, ξ) is a perturbation term. By using the variant of Rabinowitz’s perturbation method, under some growth conditions on f and g, we show that there are infinitely many weak solutions to the problem.