Kirchhoff–Schrödinger equations in ℝ2 with critical exponential growth and indefinite potential

DOI10.1142/S0219199720500303zbMath1479.35385arXiv1805.01587OpenAlexW3034573843WikidataQ115523115 ScholiaQ115523115MaRDI QIDQ5159132

Marcelo F. Furtado, Henrique R. Zanata

Publication date: 26 October 2021

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01587

zbMATH Keywords

Schrödinger equationKirchhoff equationTrudinger-Moser inequalityexistence of a ground state solution

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (4)

The ground state solution for biharmonic Kirchhoff-Schrödinger equations with singular exponential nonlinearities in \(\mathbb{R}^4\) ⋮ Sign-changing solutions for quasilinear elliptic equation with critical exponential growth ⋮ Existence and asymptotic behaviour for the \(2D\)-generalized quasilinear Schrödinger equations involving Trudinger-Moser nonlinearity and potentials ⋮ The ground state solutions for Kirchhoff-Schrödinger type equations with singular exponential nonlinearities in \(\mathbb{R}^N\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(n\)-Kirchhoff type equations with exponential nonlinearities
• Ground state solution for a Kirchhoff problem with exponential critical growth
• A multiplicity result for some Kirchhoff-type equations involving exponential growth condition in \(\mathbb{R}^2 \)
• Stationary nonlinear Schrödinger equations in \(\mathbb {R}^2\) with potentials vanishing at infinity
• Quasilinear nonhomogeneous Schrödinger equation with critical exponential growth in \({\mathbb R}^n\)
• Adams type inequalities and related elliptic partial differential equations in dimension four
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space
• Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\)
• Nodal solutions for singularly perturbed equations with critical exponential growth
• The concentration-compactness principle in the calculus of variations. The limit case. I
• A nonhomogeneous elliptic problem involving critical growth in dimension two
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• Existence and multiplicity of solutions of semilinear elliptic equations in \(\mathbb{R}^N\)
• Multiple solutions of a Kirchhoff type elliptic problem with the Trudinger-Moser growth
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs
• On singular Trudinger-Moser type inequalities for unbounded domains and their best exponents
• Multiple solutions for \(N\)-Kirchhoff type problems with critical exponential growth in \(\mathbb{R}^N\)
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• Critical points for a functional involving critical growth of Trudinger-Moser type
• A singular Moser-Trudinger embedding and its applications
• Bound States of 2-D Nonlinear Schrödinger Equations with Potentials Tending to Zero at Infinity
• On a class of singular Trudinger-Moser type inequalities and its applications
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• ON A CLASS OF QUASILINEAR HYPERBOLIC EQUATIONS
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$

This page was built for publication: Kirchhoff–Schrödinger equations in ℝ2 with critical exponential growth and indefinite potential