Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent
In this paper, ground-state solutions to a Hartree–Fock type system with a critical growth are studied. Firstly, instead of establishing the local Palais–Smale (P.-S.) condition and estimating the mountain-pass critical level, a perturbation method is used to recover compactness obtain the existenc...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11058 |
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| _version_ | 1841533490404786176 |
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| author | Xiaoli Zhu Zushun Min |
| author_facet | Xiaoli Zhu Zushun Min |
| author_sort | Xiaoli Zhu |
| collection | DOAJ |
| description | In this paper, ground-state solutions to a Hartree–Fock type system with a critical growth are studied. Firstly, instead of establishing the local Palais–Smale (P.-S.) condition and estimating the mountain-pass critical level, a perturbation method is used to recover compactness obtain the existence of ground-state solutions. To achieve this, an important step is to get the right continuity of the mountain-pass level on the coefficient in front of perturbing terms. Subsequently, depending on the internal parameters of coupled nonlinearities, whether the ground state is semi-trivial or vectorial is proved. |
| format | Article |
| id | doaj-art-77857c7b48494b21a17f8f1f7658c10c |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-77857c7b48494b21a17f8f1f7658c10c2025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-09-0120245111210.14232/ejqtde.2024.1.5111058Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponentXiaoli Zhu0Zushun MinSchool of Mathematics and Statistics Sciences, Shanxi University, Taiyuan, Shanxi, P.R. ChinaIn this paper, ground-state solutions to a Hartree–Fock type system with a critical growth are studied. Firstly, instead of establishing the local Palais–Smale (P.-S.) condition and estimating the mountain-pass critical level, a perturbation method is used to recover compactness obtain the existence of ground-state solutions. To achieve this, an important step is to get the right continuity of the mountain-pass level on the coefficient in front of perturbing terms. Subsequently, depending on the internal parameters of coupled nonlinearities, whether the ground state is semi-trivial or vectorial is proved.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11058hartree–fock systemsground-state solutionscritical growth |
| spellingShingle | Xiaoli Zhu Zushun Min Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent Electronic Journal of Qualitative Theory of Differential Equations hartree–fock systems ground-state solutions critical growth |
| title | Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent |
| title_full | Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent |
| title_fullStr | Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent |
| title_full_unstemmed | Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent |
| title_short | Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent |
| title_sort | ground state solutions of a hartree fock type system involving critical sobolev exponent |
| topic | hartree–fock systems ground-state solutions critical growth |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11058 |
| work_keys_str_mv | AT xiaolizhu groundstatesolutionsofahartreefocktypesysteminvolvingcriticalsobolevexponent AT zushunmin groundstatesolutionsofahartreefocktypesysteminvolvingcriticalsobolevexponent |