ACCEPTED AND PUBLISHED RESEARCH PAPERS:
2025
Garain, Prashanta; Gol'dshtein Vladimir; Ukhlov Alexander, On the weighted non-linear Steklov eigenvalue problem in outward cuspidal domains, (accepted in European Journal of Mathematics).
Garain, Prashanta; Ukhlov, Alexander; Estimates of variational eigenvalues on metric measure spaces, (accepted in Journal of Mathematical Sciences).
Anthal Chand, Gurdev; Garain, Prashanta; Symmetry, existence and regularity results for a class of mixed local-nonlocal semilinear singular elliptic problem via variational characterization, Math. Z. 311 (2025), no. 1, Paper No. 20, 35 pp.
Garain, Prashanta; Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations, Nonlinear Anal. 256 (2025), Paper No. 113796, 31 pp.
Biswas, Sanjit ; Garain, Prashanta; Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data, (accepted in Communications in Contemporary Mathematics, https://doi.org/10.1142/S0219199725500282).
Garain, Prashanta; Lindgren, Erik; Tavakoli, Alireza; Higher Hölder regularity for a subquadratic nonlocal parabolic equation, J. Differ. Equations 419, 253-290 (2025).
2024
Garain, Prashanta; Pchelintsev Valerii, Ukhlov Alexander, On (p,q)-eigenvalues of the weighted p-Laplace operator in outward Hölder cuspidal domains, Rev. Mat. Complut. 38 (2025), no. 2, 481–504.
Garain Prashanta; Pchelintsev Valerii, Ukhlov Alexander, On the Neumann (p,q) -eigenvalue problem in Hölder singular domains, Calc. Var. Partial Differential Equations 63 (2024), no. 7, Paper No. 172, 17 pp.
Garain Prashanta, Lindgren Erik; Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case, Math. Ann. 390 (2024), no. 4, 5753–5792.
Garain, Prashanta; Mixed anisotropic and nonlocal Sobolev type inequalities with extremal, J. Math. Sci., New York 281, No. 5, 633-645 (2024).
Garain, Prashanta, Kim, Wontae, Kinnunen, Juha; On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems, Forum Math. 36, No. 3, 697-715 (2024).
Garain, Prashanta; On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem, Manuscr. Math. 174, No. 1-2, 141-158 (2024).
Garain, Prashanta; Kinnunen, Juha; On the regularity theory for mixed local and nonlocal quasilinear parabolic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 25 (2024), no. 1, 495–540.
2023
Garain Prashanta and Ukhlov Alexander; Mixed anisotropic and nonlocal Dirichlet (p; q)-eigenvalue problem, Riv. Math. Univ. Parma (N.S.) 14 (2023), no. 1, 217–232.
Banerjee, Agnid, Garain, Prashanta, Kinnunen, Juha, Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations, Commun. Contemp. Math. 25 (2023), no. 8, Paper No. 2250032, 23 pp.
Garain, Prashanta, On a class of weighted anisotropic p-Laplace equation with singular nonlinearity, Topol. Methods Nonlinear Anal. 61 (2023), no. 2, 775–799.
Garain, Prashanta; On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity, J. Geom. Anal. 33 (2023), no. 7, Paper No. 212, 20 pp.
Garain Prashanta and Ukhlov Alexander; Mixed local and nonlocal Dirichlet (p,q)-eigenvalue problem, J. Math. Sci. (N.Y.)270, Problems in mathematical analysis. No. 123 (2023), no.6, 782–792.
Garain, Prashanta; Kinnunen, Juha; Weak Harnack inequality for a mixed local and nonlocal parabolic equation, J. Differential Equations 360 (2023), 373–406.
Garain, Prashanta; Lindgren, Erik; Higher H\"older regularity for mixed local and nonlocal degenerate elliptic equations, Calc. Var. Partial Differential Equations 62 (2023), no.2, Paper No. 67, 36 pp.
Garain, Prashanta; Mukherjee, Tuhina, On an anisotropic double phase problem with singular and sign changing nonlinearity, Nonlinear Anal. Real World Appl.70 (2023), Paper No. 103790, 28 pp.
Bal, Kaushik; Garain, Prashanta; Weighted anisotropic Sobolev inequality with extremal and associated singular problems, Differential Integral Equations 36 (2023), no.1-2, 59–92.
Garain, Prashanta; Nyström, Kaj; On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients, Math. Eng. 5 (2023), no.2, Paper No. 043, 37 pp.
2022
Ait Mahiout, Karima; Alves O., Claudianor; Garain, Prashanta; Multiple solutions for a class of quasilinear problems with double criticality, Proc. Edinb. Math. Soc. (2) 65 (2022), no.4, 1011–1047.
Garain, Prashanta, Ukhlov, Alexander, On (p,q)-eigenvalues of subelliptic operators on homogeneous Lie groups, Trans. A. Razmadze Math. Inst.176 (2022), no.2, 207–216.
Garain, Prashanta; Ukhlov, Alexander; Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems, Nonlinear Anal.223 (2022), Paper No. 113022, 35 pp.
Garain, Prashanta; Ukhlov, Alexander; Singular subelliptic equations and Sobolev inequalities on Nilpotent Lie groups, Anal. Math. Phys.12 (2022), no.2, Paper No. 67, 18 pp.
Garain, Prashanta; Kinnunen, Juha; On the regularity theory for mixed local and nonlocal quasilinear elliptic equations, Trans. Amer. Math. Soc.375 (2022), no.8, 5393–5423.
Banerjee, Agnid; Garain, Prashanta; Kinnunen, Juha; Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation, Ann. Mat. Pura Appl. (4) 201 (2022), no.4, 1717–1751.
Bal, Kaushik and Garain, Prashanta; Weighted and anisotropic Sobolev inequality with extremal, Manuscripta Math.168 (2022), no.1-2, 101–117.
Garain, Prashanta; On a degenerate singular elliptic problem, Math. Nachr. 295 (2022), no.7, 1354–1377.
2021
Bal, Kaushik; Garain, Prashanta; Mukherjee, Tuhina; On an anisotropic p-Laplace equation with variable singular exponent, Adv. Differential Equations 26 (2021), no.11-12, 535–562.
Garain, Prashanta; Kinnunen, Juha; Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces, Proc. Amer. Math. Soc.149 (2021), no.8, 3407–3416.
Alves, Claudianor O.; Garain, Prashanta and Vicentiu D. Radulescu; High perturbations of quasilinear problems with double criticality, Math. Z. 299 (2021), no.3-4, 1875–1895.
Bal, Kaushik; Garain, Prashanta; Mandal, Indubaran and Sreenadh, K; Multiplicity result to a singular quasilinear Schr\"odinger equation, J. Math. Anal. Appl.497 (2021), no.2, Paper No. 124904, 20 pp.
Garain, Prashanta; Existence and nonexistence results for anisotropic p-Laplace equation with singular nonlinearities, Complex Var. Elliptic Equ.66 (2021), no.12, 2055–2075.
2020
Garain, Prashanta and Mukherjee, Tuhina; Quasilinear nonlocal elliptic problems with variable singular exponent, Commun. Pure Appl. Anal.19 (2020), no.11, 5059–5075.
Bal, Kaushik and Garain, Prashanta; Multiplicity of solution for a quasilinear equation with singular nonlinearity, Mediterr. J. Math. 17 (2020), no. 3, Paper No. 91, 20 pp.
Garain, Prashanta and Mukherjee, Tuhina; On a class of weighted p-Laplace equation with singular nonlinearity, Mediterr. J. Math.17 (2020), no.4, Paper No. 110, 18 pp.
Garain, Prashanta; Properties of solutions to some weighted p-Laplacian equation, Opuscula Math.40 (2020), no.4, 483–494.
2019
Bal, Kaushik and Garain, Prashanta; Nonexistence results for the weighted p-Laplace equation with singular nonlinearities, Electron. J. Differential Equations (2019), Paper No. 95, 12 pp.
2017
Bal, Kaushik and Garain, Prashanta, Mandal, Indubaran; Some qualitative properties of Finsler p-Laplacian, Indag. Math. (N.S.) 28 (2017), no.6, 1258–1264.
SUBMITTED RESEARCH PAPERS:
Garain, Prashanta; On mixed local-nonlocal Sobolev-type inequalities and their connection with singular equations in the Heisenberg group.
Garain, Prashanta; Mixed local-nonlocal $p$-Laplace equation with variable singular nonlinearity in the Heisenberg group.
Chlebicka, Iwona; Garain, Prashanta; Kim, Wontae; Gradient higher integrability of bounded solutions to parabolic double-phase systems.
Garain, Prashanta; Two alternative proofs of weak Harnack inequality for mixed local and nonlocal p-Laplace equations with a nonhomogeneity, arXiv:2510.04065.
Garain, Prashanta and Lindgren, Erik; Higher H\"older regularity for fractional $(p,q)$-Laplace equations, arXiv:2509.15988.
Garain, Prashanta; Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group, arXiv:2508.19811.
Biswas, Sanjit and Garain, Prashanta; Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures, arXiv:2507.04260.
Anthal Chand, Gurdev; Garain, Prashanta; Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications, arXiv:2506.08667.