10 papers
A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth
Shaoxiong Chen, Sekhar Ghosh, Vishvesh Kumar +1
We study a two-dimensional Choquard equation driven by the mixed local and nonlocal operator , where the nonlinearity has critical exponential growth of Trudinger--…
Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper addresses the existence of nontrivial solutions to a class of mixed local-nonlocal problems involving a mixed interpolated Hardy potential. We first establish a concentr…
Harnack inequality for superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
The main aim of this paper is to establish the Hölder continuity and the Harnack inequality for weak solutions to Dirichlet problems associated with superposition operators of mix…
Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition opera…
Regularity of superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of…
Multiplicity of Solutions to the Brezis-Nirenberg Problem on Hyperbolic Spaces
Sekhar Ghosh, Vishvesh Kumar, Tapendu Rana
This article investigates the multiplicity of solutions to the Brezis-Nirenberg problem on smooth bounded domains in the hyperbolic space for . Specifically…