Publications
Sign changing solutions of the Brezis-Nirenberg problem in the hyperbolic space, (with K. Sandeep), Calculus of Variations and Partial Differential Equations, 2014, Volume 50, 69-91.
Sign changing solutions of the Hardy-Sobolev-Maz’ya equation, Advances in Nonlinear Analysis, 2014, Volume 3, Issue 3, Pages 187-196.
Nondegeneracy of positive solutions of a semilinear elliptic problem in the hyperbolic space, (With K. Sandeep), Communications in Contemporary Mathematics, 2015, Volume 17, No. 1, 1450019, 13 pages.
Improved higher order Poincare inequalities on the hyperbolic space via Hardy-type remainder terms, (with Elvise Berchio), Communications on Pure and Applied Analysis, 2016, Volume 15, Number 5, 1871-1892.
Existence results for semilinear problems in the two-dimensional hyperbolic space involving critical growth, (with Debabrata Karmakar), Proceedings of the Royal Society of Edinburgh: Section A, Volume 147 (2017), no. 1, 141-176.
Sharp Poincare-Hardy and Poincare-Rellich inequalities on the hyperbolic space, (with Elvise Berchio and Gabriele Grillo), Journal of Functional Analysis, Volume 272, Issue 4, 2017, Pages 1661-1703.
Improved Lp-Poincare inequalities on the hyperbolic space, (with Elvise Berchio, Lorenzo D’Ambrosio and Gabriele Grillo), Nonlinear Analysis, Volume 157, July 2017, Pages 146-166.
On Green functions of second-order elliptic operators on Riemannian manifolds: The critical case, (with Yehuda Pinchover), Journal of Functional Analysis, Volume 274, Issue 9, 2018, Pages 2700 - 2724.
Some Liouville-type results for eigenfunctions of elliptic operators, (with Ari Arapostathis and Anup Biswas), Trans. Amer. Math. Soc. 371 (2019), 4377-4409.
Improved multipolar Poincare-Hardy inequalities on Cartan-Hadamard manifolds, (with Elvise Berchio, Gabriele Grillo), Annali di Matematica Pura ed Applicata. 4 (2020), no. 1, 65-80.
Some new aspects of perturbation theory of positive solutions of second-order linear elliptic equations, (with Yehuda Pinchover), published in a special issue dedicated to the memory of A. I. Volpert, Pure Appl. Funct. Anal. (PAFA), Volume 5, (2020), no. 2, 295-319.
On the Equivalence of heat kernels of second-order parabolic operators, (with Yehuda Pinchover), Journal d’Analyse Mathématique 140 (2020), no.2, 549-589.
On some strong Poincaré inequalities on Riemannian models and their improvements, (with E. Berchio, P. Roychowdhury), Journal of Mathematical Analysis and Applications, (2020), no.1, 124213.
Integral representation using Green function for fractional Hardy equations, (with M. Bhakta, A. Biswas, L. Montoro), Journal of Differential Equations, 269 (2020), no.7, 5573-5594.
An Optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds, (Elvise Berchio, Gabriele Grillo and Yehuda Pinchover), Proceedings of the Royal Society of Edinburgh: Section A, 150 (2020), no. 4, 1699–1736.
The Fractional Porous Medium Equation on the hyperbolic space, (with E. Berchio, M. Bonforte, G. Grillo), (2020), Calc.Var. Partial Differential Equations, 59 (2020), 36 pp.
On the first frequency of reinforced partially hinged plates, (with E. Berchio, A. Falocchi, A, Ferrero), Commun. Contemp. Math. 23 (2021), no.3, 37 pp.
Existence and Multiplicity of positive solutions of certain nonlocal scalar field equations, (with M. Bhakta, S. Chakraborty), Mathematische Nachrichten 296 (2023), no. 9, 3816-3855.
Hardy-Rellich and second-order Poincare identities on the hyperbolic space via Bessel pairs, (E. Berchio, P. Roychowdhury), Calc.Var. Partial Differential Equations 61 (2022).
Stochastic completeness and $L^1$-Liouville property for second-order elliptic operators, (Y. Pinchover, P. Roychowdhury), 2022 arXiv: 2203.06493, in a special volume dedicated to J.A. Goldstein, Discrete Contin. Dyn. Syst. Ser. S. 17 (2024), no. 5-6, 1672–1685.
Fractional Hardy Equations with Critical and Supercritical exponents, (M. Bhakta, L. Montoro), Annali di Matematica Pura ed Applicata, 202, (2023), no.1, 397–430.
Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space, (D. Gupta, K. Sreenadh), Journal of Geometric Analysis, 33 (2023) no. 3, Paper No. 79, 27 pp.
Improved Poincare-Hardy inequalities on certain subspaces of the Sobolev space, (P. Roychowdhury), Proc. Amer. Math. Soc, 151 (2023), no. 8, 3513-3527.
Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up, (D. Karmakar, S.Mazumdar), Advances in Differential Equations, 28, (2023), 9-10, 779-805.
Classification of radial solutions to $-Δ_g u=e^u$ on Riemannian models, (E. Berchio, A. Ferrero, P. Roychowdhury), Journal of Differential Equations, 361 (2023), 417-448.
Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space, (D. Gupta, K. Sreenadh), to appear in Proceedings of the Royal Society of Edinburgh: Section A. (2025).
On a class of elliptic equations with critical perturbations in the hyperbolic space, (D. Gupta, K. Sreenadh), Asymptot. Anal. 138 (2024), no. 4, 225-253.
Global compactness result and multiplicity of solutions for a class of critical exponent problems in the hyperbolic space, (M. Bhakta, D. Gupta, A. Sahoo), Commun. Contemp. Math. 27 (2025) no. 7, Paper No. 2450045.
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows, (M. Bhakta, D. Karmakar, S. Mazumdar), Calc.Var. Partial Differential Equations, Vol 64, No 23, 2025.
Fractional Schrödinger equations with mixed nonlinearities: asymptotic profiles, uniqueness and nondegeneracy of ground states, (M. Bhakta, P. Das), Journal of Geometric Analysis, 35, (2025), no. 8, Paper No. 245.
Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space, (M. Bhakta, D. Karmakar, S. Mazumdar), Adv. Math. 479 (2025), Paper No. 110447.
Submitted/Preprints
Hardy and Rellich identities and inequalities for Grushin operators via spherical vector fields and Bessel pairs, (K. Jotsaroop, P. Roychowdhury), 2024, arXiv: 2404.05510.
Poincaré-Sobolev equations with the critical exponent and potential in the hyperbolic space, (M. Bhakta, D. Gupta, A. Sahoo), 2024, arXiv: 2410.03164.
Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space, (A. Do, N. Lam, G. Lu), 2024, arXiv: 2410.21039.