-
Previous Article
Nodal bubble-tower solutions to radial elliptic problems near criticality
- DCDS Home
- This Issue
- Next Article
A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential
| 1. | Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma |
| 2. | Dipartimento di Matematica Universitµa di Roma I, Piazza A. Moro 2, 00185 Roma, Italy |
| 3. | Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain |
$ -\text{div}( M(x)\nabla u)- a\frac{u}{|x|^2}=f \text{ in } \Omega, \qquad u=0 \text{ on } \partial \Omega$,
with respect to the summability of $f$ and the value of the parameter $a$. Here $\Omega$ is a bounded domain in $\mathbb{R}^N$ containing the origin.
| [1] |
Fengshuang Gao, Yuxia Guo. Multiple solutions for a critical quasilinear equation with Hardy potential. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 1977-2003. doi: 10.3934/dcdss.2019128 |
| [2] |
Roman Chapko, B. Tomas Johansson. On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach. Inverse Problems and Imaging, 2012, 6 (1) : 25-38. doi: 10.3934/ipi.2012.6.25 |
| [3] |
Yu Su. Ground state solution of critical Schrödinger equation with singular potential. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3347-3371. doi: 10.3934/cpaa.2021108 |
| [4] |
Xu Liu, Jun Zhou. Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity. Electronic Research Archive, 2020, 28 (2) : 599-625. doi: 10.3934/era.2020032 |
| [5] |
Boumediene Abdellaoui, Ahmed Attar. Quasilinear elliptic problem with Hardy potential and singular term. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1363-1380. doi: 10.3934/cpaa.2013.12.1363 |
| [6] |
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 |
| [7] |
Jian Zhang, Shihui Zhu, Xiaoguang Li. Rate of $L^2$-concentration of the blow-up solution for critical nonlinear Schrödinger equation with potential. Mathematical Control and Related Fields, 2011, 1 (1) : 119-127. doi: 10.3934/mcrf.2011.1.119 |
| [8] |
Guoqing Zhang, Jia-yu Shao, Sanyang Liu. Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights. Communications on Pure and Applied Analysis, 2011, 10 (2) : 571-581. doi: 10.3934/cpaa.2011.10.571 |
| [9] |
Yutian Lei, Congming Li, Chao Ma. Decay estimation for positive solutions of a $\gamma$-Laplace equation. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 547-558. doi: 10.3934/dcds.2011.30.547 |
| [10] |
Chao Zhang, Xia Zhang, Shulin Zhou. Gradient estimates for the strong $p(x)$-Laplace equation. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 4109-4129. doi: 10.3934/dcds.2017175 |
| [11] |
Jann-Long Chern, Yong-Li Tang, Chuan-Jen Chyan, Yi-Jung Chen. On the uniqueness of singular solutions for a Hardy-Sobolev equation. Conference Publications, 2013, 2013 (special) : 123-128. doi: 10.3934/proc.2013.2013.123 |
| [12] |
Jing Zhang, Shiwang Ma. Positive solutions of perturbed elliptic problems involving Hardy potential and critical Sobolev exponent. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1999-2009. doi: 10.3934/dcdsb.2016033 |
| [13] |
Fengshuang Gao, Yuxia Guo. Infinitely many solutions for quasilinear equations with critical exponent and Hardy potential in $ \mathbb{R}^N $. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5591-5616. doi: 10.3934/dcds.2020239 |
| [14] |
Boumediene Abdellaoui, Daniela Giachetti, Ireneo Peral, Magdalena Walias. Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary: Interaction with a Hardy-Leray potential. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1747-1774. doi: 10.3934/dcds.2014.34.1747 |
| [15] |
Vladimir Georgiev, Sandra Lucente. Focusing nlkg equation with singular potential. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1387-1406. doi: 10.3934/cpaa.2018068 |
| [16] |
Zifei Shen, Fashun Gao, Minbo Yang. On critical Choquard equation with potential well. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3567-3593. doi: 10.3934/dcds.2018151 |
| [17] |
Yang Liu, Wenke Li. A family of potential wells for a wave equation. Electronic Research Archive, 2020, 28 (2) : 807-820. doi: 10.3934/era.2020041 |
| [18] |
Gang Li, Fen Gu, Feida Jiang. Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1449-1462. doi: 10.3934/cpaa.2020071 |
| [19] |
Samia Challal, Abdeslem Lyaghfouri. Hölder continuity of solutions to the $A$-Laplace equation involving measures. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1577-1583. doi: 10.3934/cpaa.2009.8.1577 |
| [20] |
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1285-1301. doi: 10.3934/cpaa.2012.11.1285 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]