Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian
In this paper, we are concerned with the existence and properties of ground states for the quasilinear Schrödinger–Poisson system with combined critical nonlinearities −Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|p∗−2uin ℝ3,−Δϕ=|u|pin ℝ3, having prescribed mass ∫ℝ3|u|pdx=ap, in the Sobolev critical case. Her...
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World Scientific Publishing
2025-08-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360725500067 |
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| author | Kai Liu Xiaoming He |
| author_facet | Kai Liu Xiaoming He |
| author_sort | Kai Liu |
| collection | DOAJ |
| description | In this paper, we are concerned with the existence and properties of ground states for the quasilinear Schrödinger–Poisson system with combined critical nonlinearities −Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|p∗−2uin ℝ3,−Δϕ=|u|pin ℝ3, having prescribed mass ∫ℝ3|u|pdx=ap, in the Sobolev critical case. Here, [Formula: see text] and [Formula: see text], [Formula: see text] are parameters, [Formula: see text] is the Sobolev critical exponent, and [Formula: see text] is an undetermined parameter, appeared as a Lagrange multiplier. By using Jeanjean’s theory, Pohozaev manifold analysis and the Brezis–Nirenberg technique to overcome the lack of compactness, we prove several existence results in the [Formula: see text]-subcritical, [Formula: see text]-critical and [Formula: see text]-supercritical perturbation [Formula: see text], under different assumptions imposed on the parameters [Formula: see text] and the mass a, respectively. To the best of our knowledge, this work seems to be the first contribution regarding the existence of normalized solutions of the Sobolev critical Schrödinger–Poisson problem with p-Laplacian, perturbed with a subcritical term in the whole space [Formula: see text]. |
| format | Article |
| id | doaj-art-1b1ad3241d764b93b815b97b07c2f9c3 |
| institution | Kabale University |
| issn | 1664-3607 1664-3615 |
| language | English |
| publishDate | 2025-08-01 |
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| spelling | doaj-art-1b1ad3241d764b93b815b97b07c2f9c32025-08-22T07:46:42ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152025-08-01150210.1142/S1664360725500067Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-LaplacianKai Liu0Xiaoming He1College of Science, Minzu University of China, Beijing 100081, P. R. ChinaCollege of Science, Minzu University of China, Beijing 100081, P. R. ChinaIn this paper, we are concerned with the existence and properties of ground states for the quasilinear Schrödinger–Poisson system with combined critical nonlinearities −Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|p∗−2uin ℝ3,−Δϕ=|u|pin ℝ3, having prescribed mass ∫ℝ3|u|pdx=ap, in the Sobolev critical case. Here, [Formula: see text] and [Formula: see text], [Formula: see text] are parameters, [Formula: see text] is the Sobolev critical exponent, and [Formula: see text] is an undetermined parameter, appeared as a Lagrange multiplier. By using Jeanjean’s theory, Pohozaev manifold analysis and the Brezis–Nirenberg technique to overcome the lack of compactness, we prove several existence results in the [Formula: see text]-subcritical, [Formula: see text]-critical and [Formula: see text]-supercritical perturbation [Formula: see text], under different assumptions imposed on the parameters [Formula: see text] and the mass a, respectively. To the best of our knowledge, this work seems to be the first contribution regarding the existence of normalized solutions of the Sobolev critical Schrödinger–Poisson problem with p-Laplacian, perturbed with a subcritical term in the whole space [Formula: see text].https://www.worldscientific.com/doi/10.1142/S1664360725500067p-Laplacian Schrödinger–Poisson systemsnormalized solutionscritical Sobolev exponentPohozaev manifold |
| spellingShingle | Kai Liu Xiaoming He Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian Bulletin of Mathematical Sciences p-Laplacian Schrödinger–Poisson systems normalized solutions critical Sobolev exponent Pohozaev manifold |
| title | Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian |
| title_full | Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian |
| title_fullStr | Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian |
| title_full_unstemmed | Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian |
| title_short | Solutions with prescribed mass for the Sobolev critical Schrödinger–Poisson system with p-Laplacian |
| title_sort | solutions with prescribed mass for the sobolev critical schrodinger poisson system with p laplacian |
| topic | p-Laplacian Schrödinger–Poisson systems normalized solutions critical Sobolev exponent Pohozaev manifold |
| url | https://www.worldscientific.com/doi/10.1142/S1664360725500067 |
| work_keys_str_mv | AT kailiu solutionswithprescribedmassforthesobolevcriticalschrodingerpoissonsystemwithplaplacian AT xiaominghe solutionswithprescribedmassforthesobolevcriticalschrodingerpoissonsystemwithplaplacian |