Publications*
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✴︎ Published (or Accepted) Articles:
On the perturbed Q-curvature problem on S4, S. Prashanth, Sanjiban Santra, and A. Sarkar, Journal of Differential Equations, 255 (2013), 2363- 2391.
Exact multiplicity for the perturbed Q-curvature problem in RN, N ≥ 5, A. Sarkar and S. Prashanth, Archiv der Mathematik, 102 (2014), 575-587.
Isolated Singularities of Polyharmonic Operator in Even Dimension, R. Dhanya and A. Sarkar, Complex Variables and Elliptic Equations, 61 (1) (2016), 55-66.
Multiple Solutions of a Fourth Order Nonhomogeneous Equation With Critical Growth in R4, A. Sarkar, Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 27, pp. 1-18.
The Fredholm alternative for the p-Laplacian in exterior domains, P. Drábek, K. Ho, and A. Sarkar, Nonlinear Analysis, 174 (2018), 17–53.
On the Eigenvalue Problem Involving the Weighted p-Laplacian in Radially Symmetric Domains, P. Drábek, K. Ho, and A. Sarkar, Journal of Mathematical Analysis and Applications, 468 (2018), 716–756.
On the Generalized Hardy-Rellich Inequalities, T.V. Anoop, Ujjal Das, and A. Sarkar, Proceedings A of the Royal Society of Edinburgh, 150 (2020), no. 2, 897–919.
Multiple solutions for a weighted p-Laplacian problem, Rohit Kumar and A. Sarkar, 2021 UNC Greensboro PDE Conference. Electron. J. Diff. Eqns., Conference 26 (2022), pp. 115-122.
On the fourth order semipositone problem in RN, Nirjan Biswas, Ujjal Das, and Abhishek Sarkar, Discrete and Continuous Dynamical Systems, 2023, 43(1): 411-434.
Degenerate Schrödinger-Kirchhoff (p, N)-Laplacian problem with singular Trudinger-Moser nonlinearity in RN, Deepak Kumar Mahanta, Tuhina Mukherjee, and Abhishek Sarkar, Forum Mathematicum, vol. 37, no. 2, 2025, pp. 459-483.
Existence of positive solutions for generalized fractional Brézis-Nirenberg problem, Rohit Kumar and Abhishek Sarkar, Topological Methods in Nonlinear Analysis, 64(2): 509-543 (2024).
On fractional system of NLS-KdV equations with Hardy potential, Rohit Kumar, Tuhina Mukherjee, and Abhishek Sarkar, Indian Journal of Pure and Applied Mathematics, 2025.
On critically coupled (s1,s2)-fractional system of Schrödinger equations with Hardy potential, Rohit Kumar, Tuhina Mukherjee, and Abhishek Sarkar, Differential and Integral Equations, Vol. 39, No. 1-2, 2025.
On the extreme value of Nehari manifold for nonlocal singular Schrödinger-Kirchhoff equations in RN, Deepak Kumar Mahanta, Tuhina Mukherjee, and Abhishek Sarkar, Complex Variables and Elliptic Equations (accepted).
On the study of (p, Q)-Laplace Choquard equations with critical Trudinger-Moser nonlinearity in HN, Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar, and Lovelesh Sharma, Analysis and Applications (accepted).
✴︎ Communicated Articles:
Characterizations of compactness and weighted eigenvalue problem associated with fractional Hardy-type inequalities, Ujjal Das, Rohit Kumar, and Abhishek Sarkar.
On sharpened singular Adams' type inequalities and applications to (p,n/2)-biharmonic equations, Deepak Kumar Mahanta, Tuhina Mukherjee, and Abhishek Sarkar.
Principal eigenvalues for the weighted p-Laplacian in RN and Antimaximum Principle, Anumol Joseph and Abhishek Sarkar.
On (p, N)-Laplace multivalued equations with critical exponential nonlinearity in RN, Ankit and Abhishek Sarkar.
On sharp singular Moser-Trudinger Moser-Trudinger type inequalities and applications to zero mass (p,Q)-Laplace subelliptic equations in the Heisenberg group, Giovany Malcher Figueiredo, Deepak Kumar Mahanta, and Abhishek Sarkar
Global branching for semilinear fractional Laplace with sublinear nonlinearity, Jefferson Abrantes, Rohit Kumar, Abhishek Sarkar.
Multiplicity results for the elliptic problem with exponential growth via nonlinear Rayleigh quotient, Abhishek Sarkar and Vinayak Mani Tripathi.
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