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Infinitely many solutions for perturbed Λγ-Laplace equations

  • Duong Trong Luyen EMAIL logo and Le Thi Hong Hanh
Published/Copyright: July 22, 2022
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Abstract

In this paper, we study the multiplicity of weak solutions to the boundary value problem

- Δ γ u = f ( x , u ) + g ( x , u ) in  Ω ,
u = 0 on  Ω ,

where Ω is a bounded domain with smooth boundary in N ( N 2 ) , f ( x , ξ ) is odd in ξ, g ( x , ξ ) is a perturbation term and Δ γ is a subelliptic operator of the type

Δ γ := j = 1 N x j ( γ j 2 x j ) , x j := x j , γ := ( γ 1 , γ 2 , , γ N ) .

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.

Funding statement: This research is funded by The International Center for Research and Postgraduate Training in Mathematics, Institute of Mathematics, Vietnam Academy of Science and Technology under the Grant ICRTM04-2021.03.

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Received: 2021-09-17
Revised: 2022-03-22
Accepted: 2022-03-29
Published Online: 2022-07-22
Published in Print: 2022-12-01

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