Research

Current research interests

I study nonnegative solutions of nonlinear boundary value problems, both ODEs and PDEs. Study of coupled system of Elliptic PDEs with Dirichlet boundary conditions, where reaction terms are asymptotically linear or superlinear at infinity, using bifurcation theory has been the recent focus of my work. I have also been working on extending existence/uniqueness/multiplicity results that are known for positone problems in bounded domains to so called exterior domains.


Published/accepted

  1. A. Abebe and M. Chhetri, A nonexistence result for a class a p-Laplacian systems in a ball, Electronic Jour. Diff. Eqns. (accepted).

  2. 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, (2022) Volume 30, Issue 6: 2121-2137

  3. M. Chhetri and F. Faraci, Strongly singular problems in exterior domains. J. Differential Equations 313 (2022), 285–313.

  4. M. Chhetri, P. Girg and E. Hollifield, Continuum of positive solutions of superlinear fractional Laplacian problems, Partial Differential Equations and Applications, (2022), 3:12.

  5. M. Chhetri, N. Mavinga and R. Pardo, Bifurcation from infinity with oscillatory nonlinearity for Neumann problems, Electronic Jour. Diff. Eqns, Special Issue 01 (2021), pp. 279--292.

  6. M. Chhetri, P. Drabek and R. Shivaji, Influence of singular weights on the asymptotic behavior of positive solutions for classes of quasilinear equations, Electron. J. Qual. Theory Differ. Equ. 2020, Paper No. 73, 23 pp. .

  7. M. Chhetri, P. Girg and E. Hollifield, Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments. Electron. J. Differential Equations 2020, Paper No. 81, 31 pp.

  8. M. Chhetri and P. Girg, Some bifurcation results for fractional Laplacian problems, Nonlinear Analysis 191 (2020), 111642, 18 pp.

  9. M. Chhetri, P. Drabek and R. Shivaji, S-shaped bifurcation diagrams in exterior domains, Positivity, (2019) 23: 1147--1164.

  10. M. Chhetri, L. Sankar, B. Son and R. Shivaji, An existence result for superlinear semipositone Laplacian systems on the exterior of a ball, Differential Integral Equations 31 (2018), no. 7-8, 643–656.

  11. M. Chhetri and P. Girg, Superlinear elliptic systems with reaction terms involving product of powers, Applied Mathematics Letters 75 (2018) 121–127. 35.

  12. M. Chhetri, P. Drabek and R. Shivaji, Analysis of positive solutions for classes of quasilinear singular problems on exterior domains, Adv. Nonlinear Anal. 6 (2017), no. 4, 447–459.

  13. M. Chhetri and P. Girg – A global bifurcation result for a class of semipositone elliptic systems, Journal of Mathematical Analysis and Applications, 453 (2017), no. 1, 255–270.

  14. M. Chhetri and P. Girg - Global bifurcation of positive solutions for a class of superlinear elliptic systems, Journal of Differential Equations, 261 (2016), no. 10, 5719–5733.

  15. M. Chhetri and P. Girg - Asymptotically linear system of three equations near resonance, Journal of Differential Equations, 261 (2016), no. 10, 5900–5922.

  16. M. Chhetri and P. Girg - On the solvability of asymptotically linear systems at resonance, Journal of Mathematical Analysis and Applications, 442 (2016), no. 2, 583–599.

  17. A. Abebe, M. Chhetri and R. Shivaji, Positive solutions for a class of multiparameter elliptic systems, Dynamics of Continuous, Discrete and Impulsive Systems (DCDS-A) 23 (2016) 273-283.

  18. M. Chhetri, P. Drabek and R. Shivaji, Existence of positive solutions for a class of p-Laplacian superlinear semipositone problem, Proceedings of the Royal Society of Edinburgh, 145A, 925-936 (2015).

  19. M. Chhetri and P. Girg, Asymptotically linear system at and near resonance, Boundary Value Problems, (2014), 2014:242.

  20. M. Chhetri and P. Drabek, Principal eigenvalue of p-Laplacian operator in exterior domain, Results in Mathematics, 66 (2014), 461-468.

  21. A. Abebe, M. Chhetri, L. Sankar and R. Shivaji, Positive solutions for a class of superlinear semipositone systems on exterior domains, Boundary Value Problems, (2014), 2014:198.

  22. M. Chhetri and P. Girg, Existence of positive solutions for a class of superlinear semipositone systems, Journal of Math. Anal. Appl., 408, (2013), 781-788.

  23. M. Chhetri, S. Raynor and S. B. Robinson, Existence of multiple positive solutions to some semipositone systems, Proceedings of the Royal Society of Edinburgh, 142(A), (2012), 39-59.

  24. M. Wilhelm*, M. Chhetri, J. Rychtar and O. Ruepell, A Game theoretical analysis of the mating Sign Behavior in the Honey Bee, Bulletin of Mathematical Biology, 73, no. 3, (2011), 626--638.

  25. M. Chhetri, N. Johnson*, O. Rueppell and J. Rychtar, Revisiting the variance-based selection model of diploid drone production for multiple mating in honey bees, Journal of Interdisciplinary Mathematics, 12 (2009) 141--160.

  26. R. Gove*, M. Hayworth*, M. Chhetri and O. Rueppell, Division of labour and social insect colony performance in relation to task and mating number under two alternative response threshold models, Insectes Sociaux, 56 (2009), 319--331.

  27. M. Chhetri and P. Girg, Existence and nonexistence of positive solutions for a class of superlinear semipositone systems, Nonlinear Analysis, 71 (2009), 4984--4996.

  28. M. Chhetri and S. B. Robinson, Existence and multiplicity of positive solutions for classes of singular Elliptic PDEs, Journal of Mathematical Analysis and Applications, 357 (2009), 176--182.

  29. M. Chhetri, P. Drabek, S. Raynor and S. B. Robinson, Nonvariational problems with critical growth, Nonlinear Analysis, 68 (2008), 2092--2103.

  30. M. Chhetri and S. B. Robinson, Multiple positive solutions for singular boundary value problems, Communications on Applied Nonlinear Analysis, 14, no. 1, (2007), 15--29.

  31. M. Chhetri and P. Girg, Nonexistence of non-negative solutions for a class of (p-1)-superhomogeneous semipositone problems, Journal of Mathematical Analysis and Applications, 322, no. 2, (2006), 957--963.

  32. M. Chhetri, S. Oruganti and R. Shivaji Existence results for a class of p-Laplacian problems with sign changing weight, Differential and Integral Equations, 18, no. 9, (2005), 991--996.

  33. M. Chhetri and R. Shivaji Existence of a positive solution for a p-Laplacian semipositone problem, Boundary Value Problems, 3 (2005), 323--327.

  34. A. Castro, M. Chhetri and R. Shivaji, Stability analysis of nonnegative solutions to classes of reaction-diffusion systems, Differential and Integral Equations, 17 (2004), 391--406.

  35. M. Chhetri, D.D. Hai and R. Shivaji, On positive solutions for classes of p-Laplacian semipositone systems, Discrete Continuous Dynamical Systems 9, no. 4, (2003), 1063--1071.

  36. M. Chhetri, S. Oruganti and R. Shivaji, Positive solutions for classes of p-Laplacian equations, Journal of Differential and Integral Equations, 16, no. 6, (2003), 757--768.

  37. D.D. Hai, C. Maya and R. Shivaji, Existence of positive solution for a class of superlinear p-Laplacian semipositone systems, Differential Integral Equations, 14, no. 2, (2001), 231--240.

  38. A. Castro, C. Maya and R. Shivaji, Positivity of nonnegative solutions for cooperative semipositone systems, Dynamic Systems and Applications, 3 (2001) (Atlanta, GA, 1999), 113--120.

  39. A. Castro, C. Maya and R. Shivaji, Nonlinear eigenvalue problems with semipositone structures, Electron. Journal of Differential Equations Conference, (1999), 33--49.

  40. A. Castro, C. Maya and R. Shivaji, An existence result for a class of sublinear semipositone systems, Dynamics of Continuous Discrete and Impulsive Systems, 7, no.4, (2000), 533--540.

  41. C. Maya and R. Shivaji, Multiple positive solutions for a class of semilinear elliptic boundary value problems, Nonlinear Analysis, 38 (1999), 497--504.

  42. V. Anuradha, C. Maya and R. Shivaji, Nonnegative solutions for a class of nonlinear boundary value problems with Neumann-Robin boundary conditions, Journal of Mathematical Analysis and Applications, 236, (1999), 94--124.

  43. C. Maya and R. Shivaji, Instability of nonnegative solutions for a class of semilinear elliptic boundary value problems, Journal of Computational & Applied Mathematics, 88 (1998), 125--128.