Multiplicity of solutions for a class of quasilinear problems involving the 1-Laplacian operator with critical growth
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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.
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1-Laplacian, Functions of bounded variation, Operator, Variational methods
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Inglês
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Journal of Differential Equations, v. 308, p. 545-574.
