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Infinitely many solutions for a class of perturbed degenerate elliptic equations involving the Grushin operator

Authors: 

Duong Trong Luyen, Nguyen Minh Tri

Source title: 
Complex Variables and Elliptic Equations, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

In this paper, we study the multiplicity of weak solutions to the boundary value problem a where Ω is a bounded domain with smooth boundary in a is odd in ξ and g(x,y,ξ) is a perturbation term. Under some growth conditions on f and g, we show that there are infinitely many weak solutions to the problem. Here we do not require that f satisfies the Ambrosetti-Rabinowitz (AR) condition. The conditions on f and g are relatively weak and our result is new even in the case α=0, i.e. for the classical Laplace equation with the Dirichlet boundary condition.