Artículos de revistas
Multiplicity of solutions for a class of quasilinear problems involving the 1-Laplacian operator with critical growth
Fecha
2022-01-25Registro en:
Journal of Differential Equations, v. 308, p. 545-574.
1090-2732
0022-0396
10.1016/j.jde.2021.11.012
2-s2.0-85119435908
Autor
Universidade Federal de Campina Grande
University of Mohamed I
Universidade Estadual Paulista (UNESP)
Institución
Resumen
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.