Professional Expreiences

• Assistant Professor, Department of Mathematics, National Institute of Technology Calicut, Kerala, India. (Aug 12, 2022 - Till date).

• Lecturer, Dept. of Mathematics, RGUKT-AP, RK Valley Campus, India, (Jul 06, 2014 - Dec 22, 2016).

Research Visits &Experiences

• Visiting Professor: Ghent University, Belgium (2026)

• Visiting Professor: Ghent University, Belgium (2025)

• Post-Doc (RA): Indian Statistical Institute, Bangalore, India (2021-22)

• Visiting Researcher: Ghent University, Belgium (2022)

My research area is Nonlinear Analysis. Specifically, I use nonlinear functional analysis, variational methods, and geometry to study elliptic problems. Some keywords in my work include variational methods, fixed point theory, mountain pass geometry, Nehari manifold, Sobolev spaces, Moser iteration, De Giorgi-Nash-Moser theory, etc. I deal with weak solutions of elliptic problems defined on Euclidean space, Lie groups, and hyperbolic spaces. My recent interests are eigenvalue problems and sharp constants in functional inequalities.

Selected Publications:

• Sekhar Ghosh, Vishvesh Kumar and Michael Ruzhansky, Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups, Mathematische Annalen, 388(4), 4201-4249 (2024).
• Sekhar Ghosh, R. Lakshmi and Chao Zhang, On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data, Journal of Differential Equations, 481, Paper No. 114634, 65 pp. (2026).
• Sekhar Ghosh, Vishvesh Kumar and Michael Ruzhansky, Best constants in subelliptic fractional  Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups, Calculus of Variations and Partial Differential Equations, 65(1), Article No. 28, 28 pp. (2026).
• Souvik Bhowmick and Sekhar Ghosh, Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data, Journal of Geometric Analysis, 35(8), Article No: 218, 46 pp. (2025).
• Sekhar Ghosh and Vishvesh Kumar, Critical equations involving nonlocal subelliptic operators on stratified Lie groups: Spectrum, bifurcation and multiplicity, Israel Journal of Mathematics, (To appear), (2025).

All Publications:

25. V. D. Varma, S. K. Nadupuri, N. Chamakuri and Sekhar Ghosh, Existence and uniqueness of solution of the fluidized bed spray granulation model, The Journal of Analysis, (2026).

24. Souvik Bhowmick, Sekhar Ghosh and Vishvesh Kumar, Superlinear problems involving nonlinear superposition operators of mixed fractional order, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (2026).

23. R. Lakshmi and Sekhar Ghosh, Equivalence of weak and viscosity solutions to mixed local and nonlocal p-Laplace equation, Zeitschrift für Analysis und ihre Anwendungen, (2026).

22. Sekhar Ghosh and Vishvesh Kumar, Nonlocal subelliptic systems involving concave-convex nonlinearities on stratified Lie groups, Bulletin of Mathematical Sciences, (2026).

21. Sekhar Ghosh and Vishvesh Kumar, Critical equations involving nonlocal subelliptic operators on stratified Lie groups: Spectrum, bifurcation and multiplicity, Israel Journal of Mathematics, (To appear), (2025).

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20. Souvik Bhowmick and Sekhar Ghosh, On sign-changing solutions for mixed local and nonlocal p-Laplace operator, Discrete and Continuous Dynamical Systems Series S, 34, 28-69, (2027).

19. Souvik Bhowmick, Sekhar Ghosh and Vishvesh Kumar, Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent, Discrete and Continuous Dynamical Systems Series S,  31, 264-287 (2027).

18. Sekhar Ghosh, R. Lakshmi and Chao Zhang, On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data, Journal of Differential Equations, 481, Paper No. 114634, 65 pp. (2026).

17. Sekhar Ghosh, Vishvesh Kumar and Michael Ruzhansky, Subelliptic nonlocal Brezis-Nirenberg problems on stratified Lie groups, Communications in Contemporary Mathematics, 28(8), Article No. 2550079, 38 pp. (2026).

16. R. Lakshmi, Ratan Kumar Giri and Sekhar Ghosh, A weighted eigenvalue problem for mixed local and nonlocal operators with potential, Mathematische Nachrichten, 299(2), 367-396 (2026).

15. Sekhar Ghosh, Vishvesh Kumar and Michael Ruzhansky, Best constants in subelliptic fractional  Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups, Calculus of Variations and Partial Differential Equations, 65(1), Article No. 28, 28 pp. (2026).

14. Souvik Bhowmick, Sekhar Ghosh and Kamel Saoudi, Least energy nodal solutions for mixed local-nonlocal equations involving singularity, Zeitschrift für Angewandte Mathematik und Physik, 76(6), Article No. 232, 27 pp. (2025).

13. R. Lakshmi and Sekhar Ghosh, Mixed local and nonlocal eigenvalue problems in the exterior domain, Fractional Calculus and Applied Analysis, 28(4), 1831-1866 (2025).

12. Souvik Bhowmick and Sekhar Ghosh, Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data, Journal of Geometric Analysis, 35(8), Article No: 218, 46 pp. (2025).

11. Sekhar Ghosh, Debajyoti Choudhuri and Alessio Fiscella, Existence of at least k solutions to a fractional p-Kirchhoff problem involving singularity and critical exponent, Fractional Calculus and Applied Analysis, 28(2), 1012-1039 (2025).

10. Sekhar Ghosh, Vishvesh Kumar and Michael Ruzhansky, Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups, Mathematische Annalen, 388(4), 4201-4249 (2024).

9. Sekhar Ghosh and Dumitru Motreanu, Infinitely many large solutions to a variable order nonlocal singular equation, Fractional Calculus and Applied Analysis, 25(2), 822-839 (2022).

8. Sekhar Ghosh An existence result for singular nonlocal fractional Kirchhoff-Schrödinger-Poisson system, Complex Variables and Elliptic Equations, 67(8), 1817-1846 (2022).

7. Sekhar Ghosh, Debajyoti Choudhuri and Ratan Kumar Giri,  Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity, Complex Variables and Elliptic Equations, 66(11), 1797-1817 (2021).

6. Sekhar Ghosh and Debajyoti Choudhuri, Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity, Positivity, 24(2), 463-479 (2020).

5. Sekhar Ghosh, Kamel Saoudi, Mouna Kratou and Debajyoti Choudhuri, Least energy sign-changing solution of fractional p-Laplacian problems involving singularities, Dynamics of Partial Differential Equations, 17(2), 97-115 (2020).

4. Kamel Saoudi, Sekhar Ghosh and Debajyoti Choudhuri, Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity, Journal of Mathematical Physics, 60(10), Paper No. 101509, 28 pp. (2019).

3. Sekhar Ghosh, Akasmika Panda and Debajyoti Choudhuri, Multiplicity of solutions to an elliptic problem with singularity and measure data, Electronic Journal of Differential Equations, 2019(60), 21 pp. (2019).

2. Sekhar Ghosh, Debajyoti Choudhuri and Ratan Kumar Giri, Singular nonlocal problem involving measure data, Bulletin of the Brazilian Mathematical Society, New Series, 50(1), 187-209 (2019).

1. Akasmika Panda, Sekhar Ghosh and Debajyoti Choudhuri,  Elliptic partial differential equation involving a singularity and a Radon measure, The Journal of the Indian Mathematical Society, 86(1-2), 95-117 (2019).

Book Chapter(s):

1. Souvik Bhowmick, Sekhar Ghosh (2026). Existence of Least Energy Nodal Solutions for p-Laplace Equations Involving Singularity, Methusalem Seminars at Ghent Analysis and PDE Center, Trends in Mathematics, vol 19. Birkhäuser, Cham. doi: 10.1007/978-3-032-22493-4_4

• Effects of Measure Data on Elliptic Partial Differential Equations with Various Singularities; ARG-MATRICS, Anusandhan National Research Foundation (ANRF), India; Tenure: April 30, 2026-- April 29, 2031; Sanctioned amount: 30 Lakhs.

• Prof. Chao Zhang– Harbin Institute of Technology, China
• Prof. Kamel Saoudi – Imam Abdul Rahman bin Faisal University, Dammam, Saudi Arabia
• Prof. Michael Ruzhansky – Ghent University, Belgium
• Prof. Vicentiu D. Radulescu – AGH University of Krakow, Poland
• Dr. Akasmika Panda – Shailabala Women's College, Cuttack, India
• Prof. Dumitru Motreanu – University of Perpignan, France
• Dr. Lamine Mbarki –University of Tunis El Manar, Tunisia
• Ms. R. Lakshmi – NIT Calicut, India
• Dr. Vishvesh Kumar –Ghent University, Belgium
• Prof. Mouna Kratou– Imam Abdul Rahman bin Faisal University, Dammam, Saudi Arabia
• Dr. Tianxiang Gou –Xi’an Jiaotong University, China
• Dr. Ratan Kumar Giri – LNMIIT, Jaipur, India
• Prof. Alessio Fiscella – Universidade Estadual de Campinas, Brazil
• Dr. Debajoyti Choudhuri – IIT Bhubaneswar, India
• Mr. Souvik Bhowmick – NIT Calicut, India
• Prof. Ismail Aydin – Sinop University, Turkey
• Mr. Yergen Aikyn – Ghent University, Belgium

Ongoing:

1. LAKSHMI R (P220223MA); January 2023 onwards.
2. SOUVIK BHOWMICK (P230197MA); August 2023 onwards.
3. MUHAMMED ADIL V K (P250654MA); January 2026 onwards.

MSc Project Students (Ongoing):

1. Topic, Project Phase 1, July 2026-ongoing,

MSc Project Students (Completed):

1. A study on the eigenvalue problems for a class of elliptic PDEs in the Sobolev spaces, Project Phase 1, July 2023-December 2023. SANJAY SHAKYA (M220598MA).
2. Existence of weak solutions to some elliptic PDEs via fixed point method, Project Phase 1, July 2023-December 2023. AVIK MAITY (M220616MA).
3. Study of nonlinear eigenvalue problem involving p-Laplacian in a bounded domain, Project Phase 2, January 2024-May 2024. SANJAY SHAKYA (M220598MA).
4. Concept of Differentiability in Banach Spaces, Mini Project, January 2024-May 2024. AJIT SINGH (M230600MA).
5. Weak and Distributional Derivatives with Applications, Project Phase 1, July 2024-December 2024. AJIT SINGH (M230600MA).
6. On Weak L^p Spaces and Its Properties, Mini Project, January 2025-May 2025, SREYA HARIHARAN (M240590MA).
7. Topological Degree Theory, Project Phase 1, July 2025-December 2025, SREYA HARIHARAN (M240590MA).
8. An Introduction to Distribution Theory, Mini Project, January 2026-May 2026, Md SADIQUE ABDULLAH (M250397MA).
9. Lax-Milgram theorem and its application, Project Phase 2, January 2026-May 2026, BITAN SIT (M241205MA).
10. On Application of Topological Degree Theory to Differential Equations, Project Phase 2, January 2026-May 2026, SREYA HARIHARAN (M240590MA).

UG (ITEP) Project Students (Completed):

1. Cantor Function and Its Properties, Major Project, July 2025-December 2025. JYOTHIKA A C (B231412ED).

2025-26 Winter Semester, Jan-Apr, 2026:

• UG (BTech courses): Mathematics IV: MA2013E, CE-01 Batch Batch and ME-01 Batch

2025-26 Monsoon Semester, Jul-Dec, 2025:

• UG (BTech courses): Mathematics III: MA2003E, PE-01 Batch
• PG courses (M.Sc Mathematics): Real Analysis: MA6201E.
• PG courses (M.Sc Mathematics): Research Methodology: MA6044E.

2024-25 Winter Semester, Jan-Apr, 2025:

• UG (BTech courses): Mathematics IV: MA2013E, CE-03 Batch, ME-03 Batch and ME-01 Batch

2024-25 Monsoon Semester, Jul-Dec, 2024:

• UG (BTech courses): Mathematics III: MA2003E, CE-02 Batch and CE-03 Batch
• PG courses (M.Tech): Mathematical Methods in System Engineering: MA6007E.

2023-24 Winter Semester, Jan-Apr, 2024:

• UG (BTech courses): Mathematics IV: MA2002D, EC-03 Batch and PE 01 Batch
• PhD Elective Courses: Sobolev Spaces with Applications: MA7256E

2023-24 Monsoon Semester, Jul-Dec, 2023:

• UG (BTech courses): Mathematics III: MA2001D, EC-01 Batch
• PG courses (M.Tech): Mathematical Methods in System Engineering: MA6007E.
• PhD Elective Courses: Calculus of Variations and PDEs: MA7257E.

2022-23 Winter Semester, Jan-Apr, 2023:

• UG (BTech courses): Mathematics IV: MA2002D, CE-04 Batch
• PG courses (MSc Mathematics): Measure and Probability:MA6322

2022-23 Monsoon Semester, Jul-Dec, 2022:

• UG (BTech courses): Mathematics III: MA2001D, ME B Batch and BT Batch

• Website: Feb 11, 2025 - Till date.
• Accreditation Related Committee: Feb 11, 2025 - Till date.
• Member of B.Tech-M.Tech Dual degree committee: Jan 03, 2023 - Till date.
• Course Co-ordinator: MA2013E Mathematics IV (Winter Semester 2024-25)
• Examinations Coordinator: Feb 11, 2023 - Feb 10, 2023.
• Planning and development- All matters related to proposed PG courses: Feb 11, 2023 - Feb 10, 2023.
• Course Co-ordinator: MA2002D Mathematics IV (Winter Semester 2022-23)

• Discrete and Continuous Dynamical Systems Series S (DCDS)

• Journal of the London Mathematical Society (JLMS)

• Journal of Fourier Analysis and Applications (JFAA)

• Complex Variables and Elliptic Equations (CVEE)

• Fractional Calculus and Applied Analysis (FCAA)

• Mediterranean Journal of Mathematics (MJM)

• Analysis and Mathematical Physics (AMP)

• ANNALI DELL'UNIVERSITA' DI FERRARA (AUDF)

• Zeitschrift für angewandte Mathematik und Physik (ZAMP)

• Bulletin of the Malaysian Mathematical Sciences Society (BMMSS)

• Qualitative Theory of Dynamical Systems (QTDS)

• Journal of Inequalities and Applications (JEA)

• Journal of Nonlinear and Variational Analysis (JNVA)

• Journal of Function Spaces (JFS)

• Open Mathematics

• MR Reviewer for MathSciNet

• Received Best Teacher Award as "Institute Excellence Award for Young Teachers 2026" at NIT Calicut.
• Offered the Research Associateship (Post-Doc) at the Indian Statistical Institute Bangalore, India.
• Offered NBHM Post-Doctoral Fellowship, Dept. of Atomic Energy (DAE), India.
• Offered a Post-Doctoral Position at the University of Ufa, Russia.
• Shortlisted and Offered the INI funding to attend the INI programme Fractional differential equations, from Jan 04 to Apr 29, 2022, at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
• Offered the NBHM PhD scholarship, Department of Atomic Energy (DAE), India.
• Qualified the CSIR-NET (JRF) in June 2013, June 2014, December 2015, June 2016.
• Qualified in GATE 2014 & GATE 2015.
• Received NBHM MA/MSC scholarship, Dept. of Atomic Energy (DAE), India.

• Life Member of Indian Mathematical Society, Membership number: L/2023/113.
• Life Member of Ramanujan Mathematical Society, Membership number: 2063.