-
Previous Article
A remark on the damped wave equation
- CPAA Home
- This Issue
-
Next Article
On a variational inequality for the Navier-Stokes operator with variable viscosity
A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation
1. | Department of Mathematics and Infomation Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi,Tokyo 192-0397 |
2. | Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi,Tokyo 192-0397, Japan |
-ħ$^2 \Delta v+($ ħ$^2\omega^2/|x|^2+V(x))v=f(v)$ in $\mathbf R^2.$
We give precise asymptotic profiles of solutions as ħ$\rightarrow 0$ by variational methods and ODE arguments.
[1] |
Linda J. S. Allen, B. M. Bolker, Yuan Lou, A. L. Nevai. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1 |
[2] |
Ryo Ikehata, Marina Soga. Asymptotic profiles for a strongly damped plate equation with lower order perturbation. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1759-1780. doi: 10.3934/cpaa.2015.14.1759 |
[3] |
Tohru Wakasa, Shoji Yotsutani. Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems. Communications on Pure and Applied Analysis, 2010, 9 (2) : 539-561. doi: 10.3934/cpaa.2010.9.539 |
[4] |
Lori Badea. Multigrid methods for some quasi-variational inequalities. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1457-1471. doi: 10.3934/dcdss.2013.6.1457 |
[5] |
Zalman Balanov, Carlos García-Azpeitia, Wieslaw Krawcewicz. On variational and topological methods in nonlinear difference equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2813-2844. doi: 10.3934/cpaa.2018133 |
[6] |
Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3909-3955. doi: 10.3934/dcds.2020036 |
[7] |
Siyao Zhu, Jinliang Wang. Asymptotic profiles of steady states for a diffusive SIS epidemic model with spontaneous infection and a logistic source. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3323-3340. doi: 10.3934/cpaa.2020147 |
[8] |
Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217 |
[9] |
Bo-Qing Dong, Zhi-Min Chen. Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 765-784. doi: 10.3934/dcds.2009.23.765 |
[10] |
Xueying Sun, Renhao Cui. Existence and asymptotic profiles of the steady state for a diffusive epidemic model with saturated incidence and spontaneous infection mechanism. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4503-4520. doi: 10.3934/dcdss.2021120 |
[11] |
Michel Chipot, Karen Yeressian. On the asymptotic behavior of variational inequalities set in cylinders. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4875-4890. doi: 10.3934/dcds.2013.33.4875 |
[12] |
Per Christian Moan, Jitse Niesen. On an asymptotic method for computing the modified energy for symplectic methods. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1105-1120. doi: 10.3934/dcds.2014.34.1105 |
[13] |
Kersten Schmidt, Ralf Hiptmair. Asymptotic boundary element methods for thin conducting sheets. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 619-647. doi: 10.3934/dcdss.2015.8.619 |
[14] |
O. Chadli, Z. Chbani, H. Riahi. Recession methods for equilibrium problems and applications to variational and hemivariational inequalities. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 185-196. doi: 10.3934/dcds.1999.5.185 |
[15] |
Raffaella Servadei, Enrico Valdinoci. Variational methods for non-local operators of elliptic type. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2105-2137. doi: 10.3934/dcds.2013.33.2105 |
[16] |
Michał Jóźwikowski, Mikołaj Rotkiewicz. Bundle-theoretic methods for higher-order variational calculus. Journal of Geometric Mechanics, 2014, 6 (1) : 99-120. doi: 10.3934/jgm.2014.6.99 |
[17] |
Dang Van Hieu, Le Dung Muu, Pham Kim Quy. New iterative regularization methods for solving split variational inclusion problems. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021185 |
[18] |
Shixiu Zheng, Zhilei Xu, Huan Yang, Jintao Song, Zhenkuan Pan. Comparisons of different methods for balanced data classification under the discrete non-local total variational framework. Mathematical Foundations of Computing, 2019, 2 (1) : 11-28. doi: 10.3934/mfc.2019002 |
[19] |
Zaihui Gan. Cross-constrained variational methods for the nonlinear Klein-Gordon equations with an inverse square potential. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1541-1554. doi: 10.3934/cpaa.2009.8.1541 |
[20] |
Jiaqing Yang, Bo Zhang, Ruming Zhang. Reconstruction of penetrable grating profiles. Inverse Problems and Imaging, 2013, 7 (4) : 1393-1407. doi: 10.3934/ipi.2013.7.1393 |
2021 Impact Factor: 1.273
Tools
Metrics
Other articles
by authors
[Back to Top]