A brief description of research work

My major interest has been in the area of semi(quasi)linear elliptic equations, especially those involving critical growth nonlinearities. I have used techniques in Calculus of variations, regularity theory and geometric measure theory in my works. Broadly, my work has fallen under the following topics:

• Nonexistence Theorems and Blow-up analysis of Palais-Smale sequences for critical nonlinearity in  ℝ2
• Strong Comparison Principle for solutions of quasilinear equations
• Multiple solutions for p-Laplace equation in a ball
• Uniqueness of least energy solutions to the critical Neumann problem in ℝN
• Perturbed Scalar curvature problem on 𝕊2
• Multiplicity results for exponential nonlinearities with a concave perturbation and convex-concave/singular type nonlinearities
• Simplicity of the principal eigenvalues obtained as Rayleigh quotient minima
• Isolated singularity for exponential type problems in two dimensions
• Sobolev versus smooth minimisers
• Bifurcation analysis for elliptic equations with a singular type nonlinearitiy
• Critical/subcritical classification of non-negative Schrodinger operators with singular potentials.