-
Previous Article
Periodic solutions for three-dimensional non-monotone cyclic systems with time delays
- DCDS Home
- This Issue
-
Next Article
Entropies of a semigroup of maps
On the profile of solutions for an elliptic problem arising in nonlinear optics
| 1. | Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, China |
| 2. | School of Mathematics, The University of New South Wales, Sydney 2052, Australia |
| 3. | School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia |
$-\Delta u + (\lambda - h(x)) u = g(x) (u^{p-1} + f(u))$ in $\ \mathbb R^N,$
$u > 0$ in $\mathbb R^N,$
$u \in H^1(\mathbb R^N),$
where $\lambda > 0$ is a parameter, $h$ and $g$ are nonnegative functions in $L^\infty(\mathbb R^N).$ We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for $\lambda$ large even if $h$ and $g$ are radially symmetric.
| [1] |
Victor Isakov, Joseph Myers. On the inverse doping profile problem. Inverse Problems and Imaging, 2012, 6 (3) : 465-486. doi: 10.3934/ipi.2012.6.465 |
| [2] |
Lisa Hollman, P. J. McKenna. A conjecture on multiple solutions of a nonlinear elliptic boundary value problem: some numerical evidence. Communications on Pure and Applied Analysis, 2011, 10 (2) : 785-802. doi: 10.3934/cpaa.2011.10.785 |
| [3] |
Dieudonné Nijimbere, Songzheng Zhao, Xunhao Gu, Moses Olabhele Esangbedo, Nyiribakwe Dominique. Tabu search guided by reinforcement learning for the max-mean dispersion problem. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3223-3246. doi: 10.3934/jimo.2020115 |
| [4] |
Miao Chen, Youyan Wan, Chang-Lin Xiang. Local uniqueness problem for a nonlinear elliptic equation. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1037-1055. doi: 10.3934/cpaa.2020048 |
| [5] |
Rafał Celiński, Andrzej Raczyński. Asymptotic profile of solutions to a certain chemotaxis system. Communications on Pure and Applied Analysis, 2020, 19 (2) : 911-922. doi: 10.3934/cpaa.2020041 |
| [6] |
Xia Huang. Stable weak solutions of weighted nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2014, 13 (1) : 293-305. doi: 10.3934/cpaa.2014.13.293 |
| [7] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2505-2518. doi: 10.3934/cpaa.2020272 |
| [8] |
E. N. Dancer, Danielle Hilhorst, Shusen Yan. Peak solutions for the Dirichlet problem of an elliptic system. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 731-761. doi: 10.3934/dcds.2009.24.731 |
| [9] |
Liping Wang, Chunyi Zhao. Solutions with clustered bubbles and a boundary layer of an elliptic problem. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2333-2357. doi: 10.3934/dcds.2014.34.2333 |
| [10] |
Liping Wang, Dong Ye. Concentrating solutions for an anisotropic elliptic problem with large exponent. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3771-3797. doi: 10.3934/dcds.2015.35.3771 |
| [11] |
Liping Wang, Juncheng Wei. Solutions with interior bubble and boundary layer for an elliptic problem. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 333-351. doi: 10.3934/dcds.2008.21.333 |
| [12] |
Walter Allegretto, Yanping Lin, Zhiyong Zhang. Convergence to convection-diffusion waves for solutions to dissipative nonlinear evolution equations. Conference Publications, 2009, 2009 (Special) : 11-23. doi: 10.3934/proc.2009.2009.11 |
| [13] |
Cheng Hou Tsang, Boris A. Malomed, Kwok Wing Chow. Exact solutions for periodic and solitary matter waves in nonlinear lattices. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1299-1325. doi: 10.3934/dcdss.2011.4.1299 |
| [14] |
Alina Ostafe, Igor E. Shparlinski, Arne Winterhof. On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences. Advances in Mathematics of Communications, 2010, 4 (3) : 369-379. doi: 10.3934/amc.2010.4.369 |
| [15] |
Chengxia Lei, Yihong Du. Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 895-911. doi: 10.3934/dcdsb.2017045 |
| [16] |
Gabriella Zecca. An optimal control problem for some nonlinear elliptic equations with unbounded coefficients. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1393-1409. doi: 10.3934/dcdsb.2019021 |
| [17] |
Chunhui Qiu, Rirong Yuan. On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5707-5730. doi: 10.3934/dcds.2017247 |
| [18] |
Martino Bardi, Paola Mannucci. On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2006, 5 (4) : 709-731. doi: 10.3934/cpaa.2006.5.709 |
| [19] |
Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla. Positive radial solutions of a nonlinear boundary value problem. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1765-1783. doi: 10.3934/cpaa.2018084 |
| [20] |
Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]