Szczegóły publikacji

Opis bibliograficzny

Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth / Quanqing Li, Vicenţiu RǍDULESCU, Wen Zhang // Nonlinearity ; ISSN 0951-7715. — 2024 — vol. 37 no. 2 art. no. 025018, s. [1], 1-28. — Bibliogr. s. 27-28, Abstr. — Publikacja dostępna online od: 2024-01-18. — V. Rǎdulescu - dod. afiliacja: University of Craiova, Romania; Brno University of Technology, Czech Republic; Zhejiang Normal University, People’s Republic of China; Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

Autorzy (3)

Słowa kluczowe

normalized ground statesprofile decompositionPohozaev manifoldSobolev critical exponent

Dane bibliometryczne

ID BaDAP151877
Data dodania do BaDAP2024-03-22
Tekst źródłowyURL
Rok publikacji2024
Typ publikacjiartykuł w czasopiśmie
Otwarty dostęptak
Creative Commons
Czasopismo/seriaNonlinearity (Bristol)


In the present paper, we investigate the existence of ground state solutions to the Sobolev critical nonlinear Schrödinger equation \begin{equation} \begin{cases} -\Delta u+\lambda u = g\left(u\right)+|u|^{2^*-2}u~~\hbox{in}\;\mathbb{R}^N,\\ \int_{\mathbb{R}^N}|u|^2dx = m^2,\qquad\qquad\qquad\qquad\qquad\qquad (P_m) \end{cases} \end{equation} where $N\unicode{x2A7E} 3$, m > 0, $2^*: = \frac{2N}{N-2}$, λ is an unknown parameter that will appear as a Lagrange multiplier, g is a mass critical or supercritical but Sobolev subcritical nonlinearity. With the aid of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in $L^2(\mathbb{R}^N)$ of radii m and the profile decomposition, we obtain a couple of the normalized ground state solution to $(P_m)$ that is independent of the sign of the Lagrange multiplier. This result complements and extends the paper by Bieganowski and Mederski (2021 J. Funct. Anal.280 108989) concerning the above problem from the Sobolev subcritical setting to the Sobolev critical framework. We also answer an open problem that was proposed by Jeanjean and Lu (2020 Calc. Var. PDE59 174). Furthermore, the asymptotic behavior of the ground state energy map is also studied.

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