Prashanth K Srinivasan

Research Interests

• Variational Methods
• Partial Differential Equations of Elliptic type

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  \(\mathbb{R}^2\)
• 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 \(\mathbb{R}^N \) , \( N ≥ 4 \)
• Perturbed Scalar curvature problem on \(\mathbb{S} ^ 2\) and the Perturbed \(Q\)-curvature problem on \( \mathbb{S}^N \); exact multiplicity result for the perturbed scalar curvature problem on \(\mathbb{S} ^N \) .
• 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.