Infinitely Many Solutions for a Fourth-Order Semilinear Elliptic Equations Perturbed from Symmetry
Infinitely Many Solutions for a Fourth-Order Semilinear Elliptic Equations Perturbed from Symmetry
Source title:
Bulletin of the Malaysian Mathematical Sciences Society, 44: 1701-1725,
2020
(ISI)
Academic year of acceptance:
2020-2021
Abstract:
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.