A Schrödinger-Poisson system with the critical growth on the first Heisenberg group

DOI10.3103/S1068362323030056zbMath1528.35052OpenAlexW4382400147MaRDI QIDQ6060275

Qingying Shi, Zhenyu Guo

Publication date: 3 November 2023

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1068362323030056

zbMATH Keywords

Heisenberg groupSchrödinger-Poisson systemexistence of a ground state

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

• Unnamed Item
• Critical growth problems with singular nonlinearities on Carnot groups
• Generalized Schrödinger-Newton system in dimension \(N\geqslant 3\): critical case
• On a system involving a critically growing nonlinearity
• Frequency functions on the Heisenberg group and the uncertainty principle and unique continuation
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• An eigenvalue problem for the Schrödinger-Maxwell equations
• Schrödinger-Hardy systems involving two Laplacian operators in the Heisenberg group
• Dual variational methods in critical point theory and applications
• Existence for \((p, q)\) critical systems in the Heisenberg group
• The Schrödinger-Poisson type system involving a critical nonlinearity on the first Heisenberg group
• Semilinear subelliptic problems with critical growth on Carnot groups
• Improved Sobolev inequalities on the Heisenberg group
• On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\)
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Critical nonlocal Schrödinger-Poisson system on the Heisenberg group
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Concentration-compactness results for systems in the Heisenberg group
• Existence and multiplicity results for quasilinear equations in the Heisenberg group
• Functional Analysis

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