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May  2021, 14(5): 1747-1756. doi: 10.3934/dcdss.2020452

On a class of semipositone problems with singular Trudinger-Moser nonlinearities

Shiqiu Fu and  Kanishka Perera ,

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

* Corresponding author: Kanishka Perera

Received  December 2019 Revised  April 2020 Published  May 2021 Early access  November 2020

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.

Keywords: Semipositone problems, singular Trudinger-Moser nonlinearities, positive solutions.
Mathematics Subject Classification: Primary: 35J20; Secondary: 35B33, 35B09.
Citation: Shiqiu Fu, Kanishka Perera. On a class of semipositone problems with singular Trudinger-Moser nonlinearities. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1747-1756. doi: 10.3934/dcdss.2020452
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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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