Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials

DOI10.1016/j.jmaa.2017.11.014zbMath1382.35114arXiv1611.06719OpenAlexW2552173557MaRDI QIDQ1684799

Giovany M. Figueiredo, Marcos T. O. Pimenta

Publication date: 12 December 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.06719

zbMATH Keywords

mountain pass theoremquasilinear elliptic problem1-Laplacian

Mathematics Subject Classification ID

Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (20)

Bounded variation solution to 1-Laplacian Kirchhoff type problem in ℝ^N ⋮ Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in \(\protect \mathbb{R}^N\) ⋮ Strauss' and Lions' type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem ⋮ On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator ⋮ Existence of solution for a class of heat equation involving the 1-Laplacian operator ⋮ A Berestycki–Lions type result for a class of problems involving the 1-Laplacian operator ⋮ Some existence results of bounded variation solutions for a 1‐biharmonic problem with vanishing potentials ⋮ On bounded variation solutions of quasi-linear 1-Laplacian problems with periodic potential in \(\mathbb{R}^N\) ⋮ Existence and profile of ground-state solutions to a 1-Laplacian problem in \(\mathbb{R}^N\) ⋮ Existence and concentration of solutions for a 1-biharmonic Choquard equation with steep potential Well in \(R^N \) ⋮ On some weighted 1-Laplacian problem on \(\mathbb{R}^N\) with singular behavior at the origin ⋮ 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 \(\mathbb{R}^N\) ⋮ Anisotropic 1-Laplacian problems with unbounded weights ⋮ Some existence results of bounded variation solutions to 1-biharmonic problems ⋮ 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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