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.