Eigenvalue problems in both local and nonlocal setup.
Nonlocal PDEs.
Functional inequalities like Hardy's, Poincar\'e, Morrey's, and Moser-Trudinger's inequalities in fractional Sobolev spaces.
Fractional Orlicz-Sobolev spaces.
The Dirichlet problem for the logarithmic p-Laplacian, to appear in Transactions of the American Mathematical Society (with B. Dyda and S. Jarohs), Link
Laplacian eigenvalues for large negative Robin parameters on domains with outward peaks, NoDEA Nonlinear Differential Equations and Applications, 32(2025), no. 6, Paper no. 129 (with K. Pankrashkin and M. Vogel), Link
On generalized eigenvalue problems of fractional (p,q)-Laplace operator with two parameters, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 155(2025), no. 4, 1385-1430 (with N. Biswas), Link
On Morrey's inequality in Sobolev-Slobodeckij spaces, Journal of Functional Analysis, 287(2024), no. 9, Paper no. 110598, 68pp (with L. Brasco and F. Prinari ), Link
A note on the supersolution method for Hardy's inequality, Revista Matemática Complutense, 37(2024), no. 2, 323 - 340 (with F. Bianchi, L. Brasco, and A. C. Zagati ), Link
A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities, Advanced Nonlinear Studies, 23(2023), no. 1, paper no. 20230103, 24 pp (with M. Bhakta and K. Perera), Link
Characterization of fractional Sobolev-Poincar\'e and (localized) Hardy inequalities, Journal of Geometric Analysis, 33(2023), no. 7, paper no. 223, Link
Remarks on the fractional Moser-Trudinger inequality, Journal d'Analyse Mathematique, 148(2022), no. 2, 447- 470, Link
Hardy and Poincar\'e inequalities in fractional Orlicz-Sobolev space, Nonlinear Analysis, 216(2022), paper no. 112697, 22 pp (with K. Bal, K. Mohanta, and P. Roy ), Link
On the best constant in fractional p- Poincar\'e inequalities on cylindrical domains, Differential and Integral Equations, 34(2021), no. 11/12, 691-712 (with K. Mohanta), Link
On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded, Asymptotic Analysis, 123(2021), no. 1-2, 79-94 (with L. Esposito and P. Roy), Link
Study of fractional Poincar\'e inequalities on unbounded domains, Discrete and Continuous Dynamical Systems. Series A, 41(2021), no. 6, 2993-3020 (with I. Chowdhury, G. Csato and P. Roy), Link