Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods

DOI10.1512/iumj.2022.71.8881zbMath1490.35165OpenAlexW4285300823MaRDI QIDQ5075670

Giovany M. Figueiredo, Marcos T. O. Pimenta

Publication date: 11 May 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2022.71.8881

zbMATH Keywords

approximation methodsvariational methods1-Laplacianexistence of nodal solutions

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62)

Related Items (6)

Existence of solution for a class of heat equation involving the 1-Laplacian operator ⋮ Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity ⋮ A Berestycki–Lions type result for a class of problems involving the 1-Laplacian operator ⋮ The existence of solutions for parabolic problem with the limiting case of double phase flux ⋮ Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator ⋮ On some weighted 1-Laplacian problem on \(\mathbb{R}^N\) with singular behavior at the origin

Cites Work

• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• Anisotropic \(p,q\)-Laplacian equations when \(p\) goes to 1
• Partial symmetry of least energy nodal solutions to some variational problems
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• A sign-changing solution for a superlinear Dirichlet problem
• Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions
• Existence and comparison results for an elliptic equation involving the 1-Laplacian and \(L^1\)-data
• Minimizing total variation flow
• The Gelfand problem for the 1-homogeneous \(p\)-Laplacian
• Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem
• Existence of a Least Energy Nodal Solution for a Class of p&q-Quasilinear Elliptic Equations
• Variational Analysis in Sobolev and BV Spaces
• On a familiy of torsional creep problems.
• Generalized Gradients and Applications
• Nonlinear Analysis - Theory and Methods
• Minimizing total variation flow
• The Dirichlet problem for a singular elliptic equation arising in the level set formulation of the inverse mean curvature flow
• On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent
• The Dirichlet problem for the total variation flow

This page was built for publication: Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods