My research interests primarily focus on nonlinear analysis and partial differential equations (PDEs), particularly on local and nonlocal elliptic problems. My current areas of interest include, but are not limited to, the following:

• Elliptic PDEs of Second and Fourth Order: This includes studying problems with critical and supercritical growth.

• Nonlocal Operators: I focus on nonlocal operators, especially those involving fractional Laplacians and fractional systems, often in conjunction with Hardy-type potentials.

• Singular and Degenerate Equations: I investigate equations like Schrödinger-Kirchhoff-type problems that exhibit nonstandard nonlinearities, including Trudinger-Moser critical growth.

• Hardy-Rellich-type Inequalities and Eigenvalue Problems: My work in this area, particularly concerning weighted Sobolev spaces and exterior or radial domains, is also significant.

• Multiplicity Results and Variational Methods: I employ Nehari manifolds to establish the existence and multiplicity of solutions to various problems.

• Moser-Trudinger Type Inequalities: I explore these inequalities on Heisenberg Groups and their applications in studying certain nonlinear PDEs.

My research integrates deep functional analysis with advanced techniques from nonlinear differential equations, enabling me to address complex analytical problems in mathematical physics and geometry.