@article{Almuthaybiri2024, 
author = {Saleh Almuthaybiri and Radhia Ghanmi and Tarek Saanouni},
title = {On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30230-30262},
keywords = {Schrödinger problem, energy-critical, nonlinear equations, fixed point method, global existence, scattering, blowup},
url = {https://www.sciopen.com/article/10.3934/math.20241460},
doi = {10.3934/math.20241460},
abstract = {This study explored the time asymptotic behavior of the Schrödinger equation with an inhomogeneous energy-critical nonlinearity. The approach follows the concentration-compactness method due to Kenig and Merle. To address the primary challenge posed by the singular inhomogeneous term, we utilized Caffarelli-Kohn-Nirenberg weighted inequalities. This work notably expanded the existing literature by applying these techniques to higher spatial dimensions without requiring any spherically symmetric assumption.}
}