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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. |
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