On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator

DOI10.1007/s00526-017-1236-3zbMath1380.35103arXiv1702.06718OpenAlexW2963996274MaRDI QIDQ1674630

Marcos T. O. Pimenta, Claudianor Oliveira Alves

Publication date: 25 October 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.06718

zbMATH Keywords

1-Laplace operatorconcentration of solutionsquasilinear problems

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (18)

Bounded variation solution to 1-Laplacian Kirchhoff type problem in ℝ^N ⋮ Strauss' and Lions' type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem ⋮ Existence, multiplicity and concentration for a class of fractional \( p \& q \) Laplacian problems in \( \mathbb{R} ^{N} \) ⋮ Existence of solution for a class of heat equation involving the 1-Laplacian operator ⋮ Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials ⋮ Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator ⋮ A Berestycki–Lions type result for a class of problems involving the 1-Laplacian operator ⋮ Bounded variation solution for a class of Kirchhoff type problem involving the 1-Laplacian operator ⋮ Existence and concentration properties for the 1-biharmonic equation with lack of compactness ⋮ Some existence results of bounded variation solutions for a 1‐biharmonic problem with vanishing potentials ⋮ Existence and profile of ground-state solutions to a 1-Laplacian problem in \(\mathbb{R}^N\) ⋮ Existence and concentration behavior of solutions to 1-Laplace equations on \(\mathbb{R}^N\) ⋮ Existence of a radial solution to a 1-Laplacian problem in \(\mathbb{R}^N\) ⋮ Sub-supersolution method for a quasilinear elliptic problem involving the 1-Laplacian operator and a gradient term ⋮ Multiplicity of solutions for a class of quasilinear problems involving the \(1\)-Laplacian operator with critical growth ⋮ Properties of the 1-polyharmonic operator in the whole space and applications to nonlinear elliptic equations ⋮ On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result ⋮ Existence and concentration of positive ground states for a 1-Laplacian problem in \(\mathbb{R}^N\)

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