Research Interest
Research Interest
My research broadly focuses on the analysis of Partial Differential Equations (PDEs). In particular, I work on both local and non-local elliptic PDEs (involving divergence and non-divergence operators). My interests include variational, non-variational, and topological methods in nonlinear PDEs, with emphasis on the existence, nonexistence, uniqueness, multiplicity, and qualitative properties of weak and viscosity solutions.
R. Biswas, A. Quaas. Nonexistence of positive supersolutions for semilinear fractional elliptic equations in exterior domains, Nonlinearity, 38, no. 9 (2025), 095007.
R. Biswas, S. Goyal, K. Sreenadh. Modified quasilinear equations with strongly singular and critical exponential nonlinearity, Advances in Nonlinear Analysis, 13, no. 1 (2024), 20240019.
R. Biswas, S. Goyal, K. Sreenadh. Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N, Journal of Geometric Analysis, 34, no. 2 (2024), article no. 54.
R. Biswas, S. Tiwari. Regularity results for Choquard equations involving fractional p-Laplacian, Mathematische Nachrichten, 296, no. 9 (2023), 4060-4085.
R. Biswas, S. Goyal, K. Sreenadh. Multiplicity results for p-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in R^N, Differential and Integral Equations, 36, no. 3-4 (2023), 247-288.
R. Biswas, A. Bahrouni, A. Fiscella. Fractional double phase Robin problem involving variable order-exponents and Logarithm-type nonlinearity, Mathematical Methods in Applied Sciences, 45, no. 17 (2022), 11272-11296.
R. Biswas, S. Bahrouni, M. L. Carvalho. Fractional double phase Robin Problem involving variable order-exponents without Ambrosetti-Rabinowitz condition, Zeitschrift für Angewandte Mathematik und Physik, 73 (2022), article no. 99.
R. Biswas, S. Goyal, K. Sreenadh. Quasilinear Choquard equations involving N-Laplacian and critical exponential nonlinearity, Mathematical Methods in Applied Sciences, 45, no. 16 (2022), 9483-9503.
R. Biswas, S. Tiwari. On a class of Kirchhoff-Choquard equations involving variable order fractional p(·)-Laplacian and without Ambrosetti-Rabinowitz type condition, Topological Methods in Nonlinear Analysis, 58 (2022), 403–439.
R. Biswas, S. Tiwari. Variable order nonlocal Choquard problem with variable exponents, Complex Variables and Elliptic Equations, 66, no. 5 (2021), 853-875.
R. Biswas, S. Tiwari. Nehari manifold approach for fractional p(·)-Laplacian system involving concave-convex nonlinearities, Electronic Journal of Differential Equations, 2020, no. 98 (2020), 1-29.
J. S. Bessa, R. Biswas, J. V. Silva, G. Sá , M. Santos, Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications, 2025.