My Research interest includes  nonlinear analysis, variational methods,  semilinear and quasilinear type elliptic partial differential equations,  non local pde, asymptotic analysis,   geometric analysis, reduced limits of measure, semilinear elliptic equations with measure data, generalized boundary trace and generalized boundary value problems.

Publications

1. Hardy-Sobolev-Mazy'a type equations in bounded domains, (with K. Sandeep), Journal of Differential Equations, Vol. 247, No. 1, 2009.

2. Hardy-Sobolev type equations for p-Laplacian, 1<p<2, in bounded domain, (with A. Biswas), Differential and Integral Equations, Vol. 24, No.     1-2, 2011.

3. Poincar'e-Sobolev equations in the hyperbolic space, (with K. Sandeep), Calc. Var. Partial Differential Equations, Vol. 44, No. 1-2, 2012.

4. Entire solutions for a class of variational problems involving the biharmonic operators and Rellich  potentials, (With Roberta Musina),  Nonlinear Analysis Vol. 75, No. 9, 2012.

5. A note on the existence and breaking symmetry of the ground state solution of Hardy-Sobolev type   equations with weighted p-Laplacian,  Advanced Nonlinear Studies Vol. 12, No 3, 2012.

6. Reduced limit for semilinear boundary value problems with measure data (With Moshe Marcus),   Journal of Differential Equations  Vol 256,  Issue 8,   2014.

7. Semilinear elliptic equations admitting similarity transformations (With Moshe Marcus),  Journal of Functional Analysis  Vol 267, Issue 10, 2014.

8. Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials , Journal of Math Analysis and Applications Vol 423,  Issue 2,  2015. 1570–1579.

9. Semilinear elliptic equation with biharmonic operator and multiple critical nonlinearities,  Advanced Nonlinear Studies Vol 15, No 4, 2015 . 

10.  Caffarelli-Kohn-Nirenberg type equations of fourth order with the critical exponent and Rellich potential, Journal of Math Analysis and Applications   Vol 433, Issue 1, 2016.

11.   Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponents,   Proc. Indian Acad. Sci. Math. Sci.  Vol 127, Issue 2, 2017.

12. Semilinear elliptic PDE’s with biharmonic operator and a singular potential,  Electron. J. Differential Equations, Vol. 2016 (2016), No. 261.

13. Multiplicity results and sign changing solutions of non local equations with concave-convex nonlinearities (with Debangana Mukherjee),  Differential and Integral Equations.  Vol 30, No. 5-6 (2017), 387--422.  

14. On singular equations with critical and supercritical exponents (with Sanjiban Santra), Journal of Differential Equations 263 (2017), no. 5, 2886–2953.

15. Semilinear nonlocal elliptic equations with critical and supercritical exponents (with Debangana Mukherjee), Commun. Pure Appl. Anal.  Vol. 16, No, 5, 2017. 

16.  Sign changing solutions of p-fractional equations with concave-convex nonlinearities (with Debangana Mukherjee),  Topol. Methods Nonlinear Anal, Volume 51, No. 2, (2018), 511–544.

17.  Profile of solutions for nonlocal equations with critical and supercritical nonlinearities  (with Debangana Mukherjee and Sanjiban Santra),   Commun. Contemp. Math. Vol. 21, No. 1 (2019).

18.  Multiplicity results for $(p, q)$ fractional Laplace equations involving critical nonlinearities (with Debangana Mukherjee),  Adv. Differential Equations   Volume 24, Numbers 3-4 (2019), 185-228. 

19. Nonlocal scalar field equations: qualitative properties, asymptotic profiles and local uniqueness of solutions (with  Debangana Mukherjee),  Journal of Differential Equations.  266 (2019) 6985–7037.

20.  Nonlinear fractional elliptic systems with boundary measure data: existence and a priori estimates (with Phuoc Tai Nguyen), Journal of Math Analysis and Applications, Vol. 475, Issue 2, ( 2019), 1614-1635

21. On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures (with Phuoc Tai Nguyen), Advances in Nonlinear Analysis, Vol. 9, Issue 1, (2020), 1480–1503.

22. Integral representation of solutions using Green function for fractional Hardy equations (with Anup Biswas, Debdip Ganguly and Luigi Montoro),   Journal of Differential Equations   269 (2020) 5573–5594.

23. Existence and Multiplicity of positive solutions of certain nonlocal scalar field equations (with Debdip Ganguly and Souptik Chakraborty),  Mathematische Nachrichten, 2023. https://doi.org/10.1002/mana.202000473

24. On multiplicity of positive solutions for nonlocal equations with critical nonlinearity (with Patrizia Pucci),  Nonlinear Analysis, vol 197, No. 8,  (2020). 

25. Nonhomogeneous systems involving critical or subcritical nonlinearities (with Souptik Chakraborty and Patrizia Pucci),  Differential and Integral Equations Vol 33, No 7-8, (2020).

26. The Maximum Principle and the Moving Plane Method,  in a special issue dedicated to Prof. Louis Nirenberg, Resonance, Vol.25, No.6, (2020).

27. Fractional Hardy-Sobolev equations with nonhomogeneous terms (with  Souptik Chakraborty  and Patrizia Pucci ),  Advances in Nonlinear Analysis Vol. 10, (2021),  no. 1, 1086–1116.

28. Semilinear fractional elliptic equations with source term and boundary measure data  (with Phuoc Tai Nguyen ), Pure Appl. Funct. Anal. (PAFA),   Vol 7, No 3, (2022), a special issue dedicated to Prof. Shmuel Agmon . 


29. Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data (with Debangana Mukherjee and Phuoc Tai Nguyen ) Journal of Differential Equations,  304 (2021), 29-72.


30. Fractional elliptic systems with critical nonlinearities (with Souptik Chakraborty,  Olimpio Hiroshi Miyagaki and Patrizia Pucci ) Nonlinearity, 34 (2021), 7540--7573.


31. On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians (with Chen, Huyuan and Hajaiej, Hichem ) J. Differential Equations, 317 (2022), 1--31.


32. Fractional Hardy equations with critical and supercritical exponents (with Debdip Ganguly and Luigi Montoro), Annali di Matematica Pura ed Applicata, 202 (2023), no. 1, 397–430 .  https://doi.org/10.1007/s10231-022-01246-2 


33. Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data (with Moshe Marcus and Phuoc Tai Nguyen), Math. Annalen, 2023, https://doi.org/10.1007/s00208-023-02764-x  


34. System of equations involving fractional $p$-Laplcian and doubly critical nonlinearities (with Kanishka Perera, Firoj SK), Advanced Nonlinear Studies, 23 (2023), no. 1. https://doi.org/10.1515/ans-2023-0103


35. Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows (with Debdip Ganguly, Debabrata Karmakar, Saikat Mazumdar), to appear in Calc. Var. Partial Differential Equations.  arXiv:2207.11024 


36. Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space  (with Debdip Ganguly, Debabrata Karmakar, Saikat Mazumdar), arXiv:2211.14618


37. Global compactness result and multiplicity of solutions for critical exponent problem in the hyperbolic space (with Debdip Ganguly, Diksha Gupta, Alok Kumar Sahoo), to appear in Commun. Contemp. Math.  arXiv:2308.06710


38. Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space (with Debdip Ganguly, Diksha Gupta, Alok Kumar Sahoo),  arXiv.2410.03164


39. Critical (p,q)-fractional problems involving a sandwich type nonlinearity (with Alessio Fiscella and Shilpa Gupta),  arXiv:2409.13986 . 


40. Fractional Schrödinger equations with mixed nonlinearities: asymptotic profiles, uniqueness and nondegeneracy of ground states (with Paramananda Das and Debdip Ganguly), arXiv.2410.03233



 Post Docs


Ph.D Students

1. Debangana Mukherjee (January, 2015--March, 2018)

2. Souptik Chakraborty (2017-2021)

3 Paramananda Das (2023--)

MS students

Arghya Rakshit (2019-20)