-
Previous Article
Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms
- DCDS-S Home
- This Issue
-
Next Article
A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II
On a class of semipositone problems with singular Trudinger-Moser nonlinearities
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA |
We prove the existence of positive solutions for a class of semipositone problems with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.
References:
| [1] |
Ad imurthi and K. Sandeep,
A singular Moser-Trudinger embedding and its applications, NoDEA Nonlinear Differential Equations Appl., 13 (2007), 585-603.
doi: 10.1007/s00030-006-4025-9. |
| [2] |
I. Ali, A. Castro and R. Shivaji,
Uniqueness and stability of nonnegative solutions for semipositone problems in a ball, Proc. Amer. Math. Soc., 117 (1993), 775-782.
doi: 10.1090/S0002-9939-1993-1116249-5. |
| [3] |
A. Ambrosetti, D. Arcoya and B. Buffoni,
Positive solutions for some semi-positone problems via bifurcation theory, Differential Integral Equations, 7 (1994), 655-663.
|
| [4] |
A. Castro, D. G. de Figueredo and E. Lopera,
Existence of positive solutions for a semipositone $p$-Laplacian problem, Proc. Roy. Soc. Edinburgh Sect. A, 146 (2016), 475-482.
doi: 10.1017/S0308210515000657. |
| [5] |
A. Castro and R. Shivaji,
Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A, 108 (1988), 291-302.
doi: 10.1017/S0308210500014670. |
| [6] |
M. Chhetri, P. Drábek and R. Shivaji,
Existence of positive solutions for a class of $p$-Laplacian superlinear semipositone problems, Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), 925-936.
doi: 10.1017/S0308210515000220. |
| [7] |
D. G. Costa, H. Ramos Quoirin and H. Tehrani,
A variational approach to superlinear semipositone elliptic problems, Proc. Amer. Math. Soc., 145 (2017), 2661-2675.
doi: 10.1090/proc/13426. |
show all references
References:
| [1] |
Ad imurthi and K. Sandeep,
A singular Moser-Trudinger embedding and its applications, NoDEA Nonlinear Differential Equations Appl., 13 (2007), 585-603.
doi: 10.1007/s00030-006-4025-9. |
| [2] |
I. Ali, A. Castro and R. Shivaji,
Uniqueness and stability of nonnegative solutions for semipositone problems in a ball, Proc. Amer. Math. Soc., 117 (1993), 775-782.
doi: 10.1090/S0002-9939-1993-1116249-5. |
| [3] |
A. Ambrosetti, D. Arcoya and B. Buffoni,
Positive solutions for some semi-positone problems via bifurcation theory, Differential Integral Equations, 7 (1994), 655-663.
|
| [4] |
A. Castro, D. G. de Figueredo and E. Lopera,
Existence of positive solutions for a semipositone $p$-Laplacian problem, Proc. Roy. Soc. Edinburgh Sect. A, 146 (2016), 475-482.
doi: 10.1017/S0308210515000657. |
| [5] |
A. Castro and R. Shivaji,
Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A, 108 (1988), 291-302.
doi: 10.1017/S0308210500014670. |
| [6] |
M. Chhetri, P. Drábek and R. Shivaji,
Existence of positive solutions for a class of $p$-Laplacian superlinear semipositone problems, Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), 925-936.
doi: 10.1017/S0308210515000220. |
| [7] |
D. G. Costa, H. Ramos Quoirin and H. Tehrani,
A variational approach to superlinear semipositone elliptic problems, Proc. Amer. Math. Soc., 145 (2017), 2661-2675.
doi: 10.1090/proc/13426. |
| [1] |
Xiyou Cheng, Zhitao Zhang. Structure of positive solutions to a class of Schrödinger systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020461 |
| [2] |
Shengbing Deng, Tingxi Hu, Chun-Lei Tang. $ N- $Laplacian problems with critical double exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 987-1003. doi: 10.3934/dcds.2020306 |
| [3] |
Craig Cowan, Abdolrahman Razani. Singular solutions of a Lane-Emden system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 621-656. doi: 10.3934/dcds.2020291 |
| [4] |
Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020436 |
| [5] |
Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020442 |
| [6] |
Anna Canale, Francesco Pappalardo, Ciro Tarantino. Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials. Communications on Pure & Applied Analysis, 2021, 20 (1) : 405-425. doi: 10.3934/cpaa.2020274 |
| [7] |
Meng Chen, Yong Hu, Matteo Penegini. On projective threefolds of general type with small positive geometric genus. Electronic Research Archive, , () : -. doi: 10.3934/era.2020117 |
| [8] |
Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020345 |
| [9] |
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380 |
| [10] |
Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi. Homogenization for nonlocal problems with smooth kernels. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020385 |
| [11] |
Feifei Cheng, Ji Li. Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 967-985. doi: 10.3934/dcds.2020305 |
| [12] |
Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020446 |
| [13] |
Susmita Sadhu. Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020342 |
| [14] |
Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 |
| [15] |
Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011 |
| [16] |
Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020046 |
| [17] |
Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020 doi: 10.3934/fods.2020018 |
| [18] |
Yi-Hsuan Lin, Gen Nakamura, Roland Potthast, Haibing Wang. Duality between range and no-response tests and its application for inverse problems. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020072 |
| [19] |
Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020048 |
| [20] |
Kha Van Huynh, Barbara Kaltenbacher. Some application examples of minimization based formulations of inverse problems and their regularization. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020074 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]