• 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
doi: 10.3934/dcdss.2020452

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

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

* Corresponding author: Kanishka Perera

Received  December 2019 Revised  April 2020 Published  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.

Citation: Shiqiu Fu, Kanishka Perera. On a class of semipositone problems with singular Trudinger-Moser nonlinearities. Discrete & Continuous Dynamical Systems - S, 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. AliA. 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. AmbrosettiD. 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. CastroD. 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. ChhetriP. 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. CostaH. 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. AliA. 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. AmbrosettiD. 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. CastroD. 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. ChhetriP. 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. CostaH. 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

[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]

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

[3]

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, , () : -. doi: 10.3934/cpaa.2020274

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

Qingfang Wang, Hua Yang. Solutions of nonlocal problem with critical exponent. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5591-5608. doi: 10.3934/cpaa.2020253

[19]

Peter Poláčik, Pavol Quittner. Entire and ancient solutions of a supercritical semilinear heat equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 413-438. doi: 10.3934/dcds.2020136

[20]

Anna Abbatiello, Eduard Feireisl, Antoní Novotný. Generalized solutions to models of compressible viscous fluids. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 1-28. doi: 10.3934/dcds.2020345

2019 Impact Factor: 1.233

Article outline

[Back to Top]