Research:

My primary research interest is nonlinear elliptic partial differential equations. Semi-linear variational elliptic equations arise from various problems in differential geometry, physics, and engineering sciences. My specific goal is to investigate the qualitative and quantitative properties of solutions of these equations. It includes the study of the existence, non-existence, multiplicity, and concentration behavior of solutions of elliptic equations in cases like critical and sub-critical Sobolev growth. I am also interested in the qualitative properties like symmetry and compactness of solutions for non-compact variational problems.

The following keywords might be used to define my current research interests: Variational method, Minimax method, Perturbation, Palais-Smale decomposition, energy estimate, and Asymptotic analysis.

Research Publications:

Hopf reduction and orbit concentrating solutions for a class of superlinear elliptic equations, J. Funct. Anal. 282 (2022), no. 12, Paper No. 109459, 32 pp. (with Bhakti B. Manna, B. Ruf, P. N. Srikanth). Article
Existence of sign-changing solutions to a Hamiltonian elliptic system in R^N, J. Math. Anal. Appl. 517 (2023), no. 2, Paper No. 126655, 20 pp. (with Bhakti B. Manna). Article
Concentration results for a singularly perturbed elliptic system with variable coefficients, Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 2889–2922 (with Bhakti B. Manna). Article
A global compactness result and multiplicity of solutions for a class of critical exponent problems in the hyperbolic space (with Mousomi Bhakta, Debdip Ganguly, Diksha Gupta ), Communications in Contemporary Mathematics arXiv:2308.06710
Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space (with Mousomi Bhakta, Debdip Ganguly, Diksha Gupta ), arXiv.2410.03164

Conference Talks :

Global compactness result and multiplicity of solutions for a class of critical exponent problem in the hyperbolic space, The 38th Annual Conference of the Ramanujan Mathematical Society, Department of Mathematics, IIT Guwahati, 2023.
Hopf Reduction and orbit concentrating solutions for a class of superlinear elliptic equations, School of Basic Science, IIT Bhubaneswar, 2023.(visit)
Existence of Sign-changing Solutions to a Hamiltonian elliptic System, Mathematics Symposium 2023, Department of Mathematics, IISER Pune, 2023.
Hopf Reduction and orbit concentrating solutions for a class of superlinear elliptic equations, The 37th Annual Conference of the Ramanujan Mathematical Society, Department of Mathematics, SSN College of Engineering, Chennai, 2022.
Hopf Reduction and orbit concentrating solutions for a class of superlinear elliptic equations, Recent advances in Mathematics and related areas, Kerala School of Mathematics (KSoM), 2022.
Concentration results for a singularly perturbed elliptic system with variable coefficients, SIAM conference PD22(poster).
Entire Non-radial Sign Changing Solutions for a Fractional Schrodinger Equation, International Conference on Dynamical Systems, Control and their Applications, IIT Roorkee, 2022.
$S^1$-concentrating solutions for a superlinear elliptic equation in $R^3$, The fourth BRICS Mathematics conference, IISER TVM-2021.

Journals:

Discrete and Continuous Dynamical Systems. Series A
Journal of Mathematical Analysis and Applications
Journal of Functional Analysis
Communications in Contemporary Mathematics

Collaborations:

Talk at BRICS Mathematics conference 2021