Multiplicity of solutions for a class of quasilinear problems involving the 1-Laplacian operator with critical growth

• Autor(a) principal: Alves, Claudianor O.
• Data de Publicação: 2022
• Outros Autores: Ourraoui, Anass, Pimenta, Marcos T.O. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.jde.2021.11.012; http://hdl.handle.net/11449/229915
• topic: 1-Laplacian; Functions of bounded variation; Operator; Variational methods

The aim of this paper is to establish two results about multiplicity of solutions to problems involving the 1-Laplacian operator, with nonlinearities with critical growth. To be more specific, we study the following problem [Formula presented] where Ω is a smooth bounded domain in RN, N≥2 and ξ∈{0,1}. Moreover, λ>0, q∈(1,1⁎) and [Formula presented]. The first main result establishes the existence of many rotationally non-equivalent and nonradial solutions by assuming that ξ=1, Ω={x∈RN:r<|x|<r+1}, N≥2, N≠3 and r>0. In the second one, Ω is a smooth bounded domain, ξ=0, and the multiplicity of solutions is proved through an abstract result which involves genus theory for functionals which are sum of a C1 functional with a convex lower semicontinuous functional.