Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms
In this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: −Δu−λu=|u|4u+μ(Iα∗|u|p)|u|p−2u,x∈ℝ3,∫ℝ3u2dx=c, where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The ma...
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World Scientific Publishing
2025-08-01
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360725500055 |
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| author | Peng Jin Heng Yang Xin’ao Zhou |
| author_facet | Peng Jin Heng Yang Xin’ao Zhou |
| author_sort | Peng Jin |
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| description | In this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: −Δu−λu=|u|4u+μ(Iα∗|u|p)|u|p−2u,x∈ℝ3,∫ℝ3u2dx=c, where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The main results in this paper are the following: (1)existence of ground state solution with negative energy for all [Formula: see text]; (2)existence of mountain-pass solution with positive energy for all [Formula: see text]; (3)existence of ground state solution for [Formula: see text] and some [Formula: see text]. |
| format | Article |
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| institution | Kabale University |
| issn | 1664-3607 1664-3615 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | World Scientific Publishing |
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| series | Bulletin of Mathematical Sciences |
| spelling | doaj-art-1d01a995a1b14e41b5a2b804db0dbc822025-08-22T07:46:41ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152025-08-01150210.1142/S1664360725500055Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard termsPeng Jin0Heng Yang1Xin’ao Zhou2School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P. R. ChinaPublic Basic Course Department, Hunan Polytechnic of Environment and Biology, Hengyang, Hunan 421005, P. R. ChinaSchool of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P. R. ChinaIn this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: −Δu−λu=|u|4u+μ(Iα∗|u|p)|u|p−2u,x∈ℝ3,∫ℝ3u2dx=c, where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The main results in this paper are the following: (1)existence of ground state solution with negative energy for all [Formula: see text]; (2)existence of mountain-pass solution with positive energy for all [Formula: see text]; (3)existence of ground state solution for [Formula: see text] and some [Formula: see text].https://www.worldscientific.com/doi/10.1142/S1664360725500055Nonlinear Schrödinger equationnormalized solutionground statevariational methodcritical nonlinearitymixed nonlinearities |
| spellingShingle | Peng Jin Heng Yang Xin’ao Zhou Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms Bulletin of Mathematical Sciences Nonlinear Schrödinger equation normalized solution ground state variational method critical nonlinearity mixed nonlinearities |
| title | Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms |
| title_full | Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms |
| title_fullStr | Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms |
| title_full_unstemmed | Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms |
| title_short | Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms |
| title_sort | normalized solutions for schrodinger equations with critical sobolev exponent and perturbations of choquard terms |
| topic | Nonlinear Schrödinger equation normalized solution ground state variational method critical nonlinearity mixed nonlinearities |
| url | https://www.worldscientific.com/doi/10.1142/S1664360725500055 |
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