- Previous Article
- CPAA Home
- This Issue
-
Next Article
In a horizontal layer with free upper surface
On existence and concentration behavior of ground state solutions for a class of problems with critical growth
| 1. | Departamento de Matematica, Universidade Federal da Paraiba, 58100-907 Campina Grande-PB, Brazil |
| 2. | Departamento de Matematica e Estatistica, Universidade Federal da Paraiba,58109-970, Brazil |
$-h^2\Delta u+V(z)u=\lambda u^q+u^{2^{ *} -1,\mathbb R^N $
$u(z)>0\quad $ for all $z\in \mathbb R^N \qquad\qquad\qquad\qquad\qquad\qquad\qquad (P_{h})$
where $h, \lambda >0$, 1<$q$ <$2^{ * -1$ $=\frac{N+2}{N-2}$, $N\geq 3$ and $V: \mathbb R^N\to \mathbb R$ is a positive function such that
0< $i nf_{z\in\mathbb R^N}V(z)$< $limi nf_{|z| \rightarrow \infty}V(z)=V_{\infty}.$
| [1] |
Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
| [2] |
Yinbin Deng, Qi Gao, Dandan Zhang. Nodal solutions for Laplace equations with critical Sobolev and Hardy exponents on $R^N$. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 211-233. doi: 10.3934/dcds.2007.19.211 |
| [3] |
Xiaorong Luo, Anmin Mao, Yanbin Sang. Nonlinear Choquard equations with Hardy-Littlewood-Sobolev critical exponents. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1319-1345. doi: 10.3934/cpaa.2021022 |
| [4] |
Yu Zheng, Carlos A. Santos, Zifei Shen, Minbo Yang. Least energy solutions for coupled hartree system with hardy-littlewood-sobolev critical exponents. Communications on Pure and Applied Analysis, 2020, 19 (1) : 329-369. doi: 10.3934/cpaa.2020018 |
| [5] |
Yanfang Peng, Jing Yang. Sign-changing solutions to elliptic problems with two critical Sobolev-Hardy exponents. Communications on Pure and Applied Analysis, 2015, 14 (2) : 439-455. doi: 10.3934/cpaa.2015.14.439 |
| [6] |
Yi He, Gongbao Li. Concentrating soliton solutions for quasilinear Schrödinger equations involving critical Sobolev exponents. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 731-762. doi: 10.3934/dcds.2016.36.731 |
| [7] |
F. R. Pereira. Multiple solutions for a class of Ambrosetti-Prodi type problems for systems involving critical Sobolev exponents. Communications on Pure and Applied Analysis, 2008, 7 (2) : 355-372. doi: 10.3934/cpaa.2008.7.355 |
| [8] |
Tsung-Fang Wu. On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function. Communications on Pure and Applied Analysis, 2008, 7 (2) : 383-405. doi: 10.3934/cpaa.2008.7.383 |
| [9] |
Minbo Yang, Fukun Zhao, Shunneng Zhao. Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5209-5241. doi: 10.3934/dcds.2021074 |
| [10] |
Yi He, Lu Lu, Wei Shuai. Concentrating ground-state solutions for a class of Schödinger-Poisson equations in $\mathbb{R}^3$ involving critical Sobolev exponents. Communications on Pure and Applied Analysis, 2016, 15 (1) : 103-125. doi: 10.3934/cpaa.2016.15.103 |
| [11] |
Xiaoli Chen, Jianfu Yang. Improved Sobolev inequalities and critical problems. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3673-3695. doi: 10.3934/cpaa.2020162 |
| [12] |
Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357 |
| [13] |
Xiaomei Sun, Yimin Zhang. Elliptic equations with cylindrical potential and multiple critical exponents. Communications on Pure and Applied Analysis, 2013, 12 (5) : 1943-1957. doi: 10.3934/cpaa.2013.12.1943 |
| [14] |
Dongsheng Kang. Quasilinear systems involving multiple critical exponents and potentials. Communications on Pure and Applied Analysis, 2013, 12 (2) : 695-710. doi: 10.3934/cpaa.2013.12.695 |
| [15] |
Mousomi Bhakta, Debangana Mukherjee. Semilinear nonlocal elliptic equations with critical and supercritical exponents. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1741-1766. doi: 10.3934/cpaa.2017085 |
| [16] |
Wenmin Gong, Guangcun Lu. On Dirac equation with a potential and critical Sobolev exponent. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2231-2263. doi: 10.3934/cpaa.2015.14.2231 |
| [17] |
Marek Fila, John R. King. Grow up and slow decay in the critical Sobolev case. Networks and Heterogeneous Media, 2012, 7 (4) : 661-671. doi: 10.3934/nhm.2012.7.661 |
| [18] |
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 |
| [19] |
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 |
| [20] |
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 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]