Existence and concentration of positive ground states for a 1-Laplacian problem in \(\mathbb{R}^N\)

DOI10.1016/j.aml.2019.106045zbMath1428.35021OpenAlexW2972569439MaRDI QIDQ2338275

Hongxia Shi, Zewei Wang, Guofeng Che

Publication date: 21 November 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.106045

zbMATH Keywords

concentration-compactness principlebounded variation functions1-Laplacian operatorNehari manifold technique

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Semilinear elliptic equations (35J61)

Related Items (12)

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR KIRCHHOFF-SCHRÖDINGER-POISSON SYSTEM WITH CONCAVE AND CONVEX NONLINEARITIES ⋮ 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 \(\protect \mathbb{R}^N\) ⋮ Bound state positive solutions for a class of elliptic system with Hartree nonlinearity ⋮ Existence and concentration properties for the 1-biharmonic equation with lack of compactness ⋮ Infinitely many solutions for the Klein-Gordon equation with sublinear nonlinearity coupled with Born-Infeld theory ⋮ Dirichlet or Neumann problem for weighted 1-Laplace equation with application to image denoising ⋮ Existence and multiplicity of positive solutions for Kirchhoff-Schrödinger-Poisson system with critical growth ⋮ Properties of the 1-polyharmonic operator in the whole space and applications to nonlinear elliptic equations ⋮ Existence of positive ground state solutions to a nonlinear fractional Schrödinger system with linear couplings ⋮ Ground state solution ofp-Laplacian equation with finite many critical nonlinearities ⋮ EXISTENCE AND CONCENTRATION RESULT FOR KIRCHHOFF EQUATIONS WITH CRITICAL EXPONENT AND HARTREE NONLINEARITY

Cites Work

• Nonlinear total variation based noise removal algorithms
• Existence and concentration result for a quasilinear Schrödinger equation with critical growth
• The total variation flow in \(\mathbb R^N\)
• On a class of nonlinear Schrödinger equations
• Parabolic quasilinear equations minimizing linear growth functionals
• 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 bounded variation solutions for a 1-Laplacian problem with vanishing potentials
• Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent
• The Euler Equation for Functionals with Linear Growth

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