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math.AP2025
Superlinear problems involving nonlinear superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar
In this work, we study a class of elliptic problems involving nonlinear superpositions of fractional operators of the form \[ A_{μ,p}u := \int_{[0,1]} (-Δ)_{p}^{s} u \, dμ(s), \] w…
math.AP2025
On sign-changing solutions for mixed local and nonlocal -Laplace operator
Souvik Bhowmick, Sekhar Ghosh
In this paper, we use the method of invariant sets of descending flows to demonstrate the existence of multiple sign-changing solutions for a class of elliptic problems with zero D…
math.AP2024
Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data
Souvik Bhowmick, Sekhar Ghosh
In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-Δu+(-Δ)^s…