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Normalized solutions for Schrödinger equations with potential and general nonlinearities involving critical case on large convex domains
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2024, Iss 53, Pp 1-53 (2024)
- Publication Year :
- 2024
- Publisher :
- University of Szeged, 2024.
-
Abstract
- In this paper, we study the following Schrödinger equations with potentials and general nonlinearities \begin{equation*} \begin{cases} -\Delta u+V(x)u+\lambda u=|u|^{q-2}u+\beta f(u), \\ \int |u|^2dx=\Theta, \end{cases} \end{equation*} both on $\mathbb{R}^N$ as well as on domains $\Omega_r$ where $\Omega_r \subset \mathbb{R}^N$ is an open bounded convex domain and $r>0$ is large. The exponent satisfies $2+\frac{4}{N}\leq q\leq2^*=\frac{2 N}{N-2}$ and $f:\mathbb{R}\rightarrow \mathbb{R}$ satisfies $L^2$-subcritical or $L^2$-critical growth. This paper generalizes the conclusion of Bartsch et al. in [4]. Moreover, we consider the Sobolev critical case and $L^2$-critical case of the above problem.
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2024
- Issue :
- 53
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.feca35162eef4d8d9bcf1ee6572a00d6
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2024.1.53