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My research centers on nonlinear elliptic boundary value problems, especially those in which the nonlinearity appears on the boundary — a setting that arises in chemical reactions, combustion, and population dynamics, and one where the analytical theory is still limited. I study these problems through both analysis and numerical methods, establishing existence, multiplicity, and bifurcation of solutions and developing finite-difference approximations to capture their structure. More recently, I have been extending these boundary-value questions beyond the continuous setting to discrete and hybrid domains through dynamic equations on time scales, which unify the differential and difference cases. A full list of my publications is available on Google Scholar.

If you have trouble accessing any of my papers through the DOI or arXiv links, feel free to email me at sbandyo5@utm.edu for a copy.

Existence, Multiplicity, Bifurcation Theory

Active Collaborators:

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  1. Nsoki Mavinga

  2. Marius N Nkashama

  3. Briceyda Delgado

  4. Maria Amarakristi Onyido

 

My core program concerns nonlinear elliptic problems with nonlinearity on the boundary, which I study through two complementary approaches: the upper–lower solution method, which applies to general nonlinearities and yields existence of maximal and minimal weak solutions, and bifurcation analysis, which I use for superlinear problems. I began with problems that are linear in the domain and nonlinear on the boundary, in the scalar case, and have extended this work from scalar equations to systems and from boundary-only nonlinearity toward problems with nonlinearity both inside the domain and on the boundary. Throughout, the nonlinear boundary condition remains the central thread; I am now extending the program to other types of nonlinearity in this setting.

Related Work

  1. S. Bandyopadhyay, B. B. Delgado, N. Mavinga, and M. A. Onyido, "Existence results for quasimonotone elliptic systems with growth up to critical exponents." Bol. Soc. Mat. Mex. 32, 91 (2026). https://doi.org/10.1007/s40590-026-00919-9
     

  2. S. Bandyopadhyay, M. Chhetri, B. Delgado, N. Mavinga, and R. Pardo, "Positive solutions of elliptic systems with superlinear nonlinearities on the boundary," (under review, 2025). arXiv:2511.04943. https://arxiv.org/abs/2511.04943
     

  3. S. Bandyopadhyay, M. Chhetri, B. B. Delgado, N. Mavinga, and R. Pardo, "Bifurcation and multiplicity results for elliptic problems with subcritical nonlinearity on the boundary," Journal of Differential Equations, 411 (2024), 28–50. https://doi.org/10.1016/j.jde.2024.07.034
     

  4. S. Bandyopadhyay, T. Lewis, and N. Mavinga, "Existence of maximal and minimal weak solutions and finite difference approximations for elliptic systems with nonlinear boundary conditions," Electronic Journal of Differential Equations, 2025 (2025), No. 43, 1–21. https://doi.org/10.58997/ejde.2025.43
     

  5. S. Bandyopadhyay, M. Chhetri, B. B. Delgado, N. Mavinga, and R. Pardo, "Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary," Electronic Research Archive, 30 (2022), No. 6, 2121–2137. https://doi.org/10.3934/era.2022107

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Numerical Approximation

Active Collaborators:

  1. Thomas L Lewis

  2. Dustin Nichols

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My numerical analysis research focuses on approximating solutions of elliptic problems using finite difference methods. I have studied both sublinear and superlinear problems. This computational work complements my theoretical research, providing a complete analytical and numerical framework for understanding elliptic problems.

Related Work

  1. S. Bandyopadhyay, T. Lewis, and D. Nichols, "Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary," (under review, 2025). arXiv:2509.08990.https://arxiv.org/abs/2509.08990
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  2. S. Bandyopadhyay, T. Lewis, and N. Mavinga, "Existence of maximal and minimal weak solutions and finite difference approximations for elliptic systems with nonlinear boundary conditions," Electronic Journal of Differential Equations, 2025 (2025), No. 43, 1–21. https://doi.org/10.58997/ejde.2025.43

Nonlinear Elliptic Partial Dynamic Equation

Active Collaborators:
 
Tom Cuchta

A frontier of my program is the study of elliptic PDEs on time scales, which unify continuous and discrete settings. I have begun with the Dirichlet problem and am progressing toward Sturm–Liouville and mixed boundary conditions. A central obstruction is that the notion of an outer normal does not yet exist on time scales, so Neumann and nonlinear boundary conditions — the boundary settings at the heart of the rest of my work — are not yet available in this context. My current effort is aimed at this gap: developing a notion of boundary flux, beginning on lattice domains.

Related Work

  1. S. Bandyopadhyay, F. A. Çetinkaya, and T. Cuchta, "Nonlinear elliptic Dirichlet boundary value problems on time scales," (Accepted in Turkish Journal of Mathematics, 2026). arXiv:2602.10335. https://arxiv.org/abs/2602.10335

Other Work

  1. S. Bandyopadhyay, S. G. Georgiev, "Nonlinear Higher-Order Dynamic Equation with Polynomial Growth and Mixed Boundary Conditions," (Accepted in Journal of Fixed Point Theory and Application, 2026). arXiv:2506.08808. https://arxiv.org/abs/2506.08808
     

  2. S. Bandyopadhyay, C. J. Kunkel, "Existence Result for Singular Second Order Dynamic Equations with Mixed Boundary Conditions," (under review, 2025). arXiv:2506.16505. https://arxiv.org/abs/2506.16505
     

  3. S. Bandyopadhyay, F. A. Çetinkaya, T. Cuchta, "Prüfer Transformation and Spectral Analysis for a Sturm–Liouville-Type Equation," (under review, 2025). arXiv:2508.12369. https://arxiv.org/abs/2508.12369
     

  4. A. Acharya, S. Bandyopadhyay, J. T. Cronin, J. Goddard II, A. Muthunayake, and R. Shivaji, "The diffusive Lotka–Volterra competition model in fragmented patches I: Coexistence," Nonlinear Analysis: Real World Applications, 70 (2023), 103775. https://doi.org/10.1016/j.nonrwa.2022.103775

Research Collaborators

Current Collaborators​

Past Collaborators

Screenshot 2025-09-29 at 4.49.47 PM.png

With Maria AmaraKristi Onyido

With Nsoki Mavinga

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With Xiang Wan
 

With Tom Cuchta

With Dr. Cuchta @MCA2025

I am fortunate to work with Dr. Tom Cuchta from Marshall University as my research mentor through the AMS Simons travel grant. Dr. Cuchta is an Assistant Professor of Mathematics whose research focuses on special functions, difference equations, and time scale calculus. Despite my being new to this field—having not worked on anything similar during my PhD—Dr. Cuchta graciously welcomed me into this research area and has been incredibly resourceful in guiding my development as a researcher.

Since we first met at the SEARCDE conference in Morgantown, West Virginia in November 2024, where he invited me to dinner and we connected over our shared interests, Dr. Cuchta has been instrumental in my research journey. When we began our collaborative project in February 2025, he not only provided expert guidance on the technical aspects of our work but also helped me navigate grant writing and connected me with other researchers and collaborators in the field. His mentorship has been invaluable in helping me establish myself in an entirely new area of mathematics, and his willingness to work with someone inexperienced in the field speaks to his dedication to fostering mathematical research and collaboration.

Research Collaboration Programs

A list of programs that support small-group collaborative research, for anyone looking for a place to work with collaborators.
 

North America
 

  • AIM SQuaREs, American Institute of Mathematics. Structured groups of four to six, returning for up to three years. aimath.org/programs/squares

  • BIRS Research in Teams and Focused Research Groups. Small teams for one to two weeks, at Banff and partner stations in Oaxaca and Kelowna. birs.ca

  • Collaborate@ICERM, Brown University. Small groups for a week or more, Providence. icerm.brown.edu

  • IAS Summer Collaborators, Institute for Advanced Study. Princeton. ias.edu/math/summercollaborators

  • SLMath PROOF, Berkeley. Two-week summer program for small groups, aimed at researchers facing heavy teaching loads, isolation, or limited funding. SLMath also runs LATTICE, a yearlong team program. slmath.org/proof
     

Europe
 

  • CIRM Research in Residence, Luminy, France. cirm-math.com/research-in-residence.html

  • Oberwolfach Research in Pairs, Germany. Two to four people, one to four weeks. mfo.de

  • Institut Henri Poincaré Research in Paris. Two to four people, one to six weeks. ihp.fr

  • ICMS Research in Groups, Edinburgh. icms.org.uk

  • Institut Mittag-Leffler Research in Peace, Sweden. mittag-leffler.se

  • Erwin Schrödinger Institute Research in Teams, Vienna. One to four months. esi.ac.at
     

Networks

  • AWM Research Networks and Research Collaboration Conferences for Women. Teams often continue at BIRS Research in Teams. awm-math.org

Research Grants and Funding

Funding opportunities for early-career mathematicians, with a focus on those at primarily undergraduate institutions.
 

  • SIAM Travel Awards. Modest travel support to attend SIAM conferences, for members who are presenting or early in their careers. Amounts vary by meeting. siam.org

  • AMS Joint Mathematics Meetings travel support. Travel assistance to attend the JMM. Categories and amounts change year to year, so confirm the current offerings. ams.org

  • AWM Travel Grants. Up to $2,300 for domestic travel and $3,500 for foreign travel, for women in mathematics. awm-math.org

  • AMS-Simons Travel Grant. $2,500 per year for two years, for mathematicians within four years of the PhD. Awarded once. ams.org

  • AMS China Exchange, Ky and Yu-Fen Fan Fund. About $2,500 to $5,000 for research travel between the US or Canada and China. ams.org

  • AWM Mentoring Travel Grants. Up to $5,000 for a junior woman to spend about a month doing research with a senior mentor. awm-math.org

  • Mary Beth Ruskai Research Fund for Women. $5,000 for 12 months, from the EDGE Foundation, prioritizing women outside major research universities. edgeforwomen.org

  • AMS-Simons Research Enhancement Grants for PUI Faculty. $3,000 per year for three years, for faculty at institutions that do not grant a math doctorate, with a PhD earned at least five years earlier. ams.org

  • Fulbright U.S. Scholar Program. Support for research or teaching abroad, amount varies by country and length. fulbrightscholars.org

  • NSF, Division of Mathematical Sciences. Core research grants in areas such as Analysis and Applied Mathematics. PUI faculty apply through the Research in Undergraduate Institutions (RUI) mechanism, with Research Opportunity Awards (ROA) for research visits to a collaborator. nsf.gov

  • NSF CAREER. A five-year award for pre-tenure faculty combining research and education. nsf.gov

Member: AMS, MAA, AWM, ISDE

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