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

Authors: 

Duong Trong Luyen

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 ⊂ a,(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.