Sharp Trudinger-Moser inequality and ground state solutions to quasi-linear Schrödinger equations with degenerate potentials in \(\mathbb{R}^n\)

DOI10.1515/ANS-2021-2146zbMath1479.35264OpenAlexW3206839311MaRDI QIDQ2240565

Guozhen Lu, Maochun Zhu, Lu Chen

Publication date: 4 November 2021

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2021-2146

zbMATH Keywords

quasi-linear Schrödinger equationexistence of ground state solutionsdegenerate potentialsharp Trudinger-Moser inequality

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Schrödinger operator, Schrödinger equation (35J10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (19)

A sharpened form of Adams-type inequalities on higher-order Sobolev spaces : a simple approach ⋮ Singular Hardy–Adams inequalities on hyperbolic spaces of any even dimension ⋮ Sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the upper half-spaces ⋮ Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces ⋮ Existence and non-existence of extremals for critical Adams inequality in any even dimension ⋮ Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group ⋮ Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-𝐿^{∞} spaces ⋮ Sharpened Trudinger-Moser inequalities on the Euclidean space and Heisenberg group ⋮ Existence of extremals for Trudinger-Moser inequalities involved with a trapping potential ⋮ Least energy solutions to quasilinear subelliptic equations with constant and degenerate potentials on the Heisenberg group ⋮ Critical and supercritical Adams' inequalities with logarithmic weights ⋮ Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials ⋮ Asymptotic properties of critical points for subcritical Trudinger-Moser functional ⋮ Equivalence of subcritical and critical Adams inequalities in \(W^{m,2}(\mathbb{R}^{2m})\) and existence and non-existence of extremals for Adams inequalities under inhomogeneous constraints ⋮ A sharp Moser-Trudinger type inequality involving \(L^p\) norm in \(\mathbb{R}^n\) with degenerate potential ⋮ Existence of sign-changing radial solutions with prescribed numbers of zeros for elliptic equations with the critical exponential growth in ℝ² ⋮ Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth ⋮ Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity ⋮ Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well

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