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Prashanth K Srinivasan

Prashanth K Srinivasan

Professor (H)

Room No.204
Office Phone: +91 80 6695-3746

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.