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Mixed local-nonlocal eigenvalue problems in the Heisenberg group: spectral theory and singular multiplicity
Prashanta Garain, Vicentiu Radulescu
This paper investigates nonlinear eigenvalue problems governed by a family of operators that combine two distinct diffusion mechanisms: a classical local diffusion, which accounts…
Mixed local and nonlocal weighted singular quasilinear elliptic problem and its associated Sobolev-type inequality
Prashanta Garain
We consider a class of mixed anisotropic and nonlocal singular quasilinear elliptic problem associated with Muckenhoupt weights. The presence of the singular nonlinearity, which bl…
On the regularity theory for mixed local and nonlocal weighted quasilinear elliptic equations
Sanjit Biswas, Prashanta Garain
We investigate a broad class of mixed local and nonlocal degenerate -Laplace equations with general right-hand sides. The degeneracy is governed by Muckenhoupt -weights, yi…
Ground state solutions of mixed local-nonlolcal equations with Hartree type nonlinearities
Gurdev Chand Anthal, Prashanta Garain, Nidhi Nidhi
We study a class of mixed local-nonlocal equations with Hartree-type nonlinearities of the form \begin{equation}\label{meqnab} -Δu + (-Δ)^s u + u = (I_α* F(u))\,F'(u) \quad \text{i…