Research Projects

This project aims to study the existence and multiplicity results of local/non-local quasi-linear and modified quasilinear elliptic partial differential equations. The study of elliptic equations involving fractional $p-$Laplace operator and non-local operators has gained attention due to their real-world applications. The project will focus on modified quasilinear operators involving Laplacian operators, Kirchoof operators, and non-local Choquard operators with critical growth problems. The multiplicity results for these operators with singular and polynomial/exponential type critical nonlinearity will be investigated. The project will also investigate the variational setup for fractional Laplacian operator and $p-q$ Laplacian. The modified Schrödinger equation will be studied with discontinuous and exponential-type nonlinearity.