6 citations · 23 across the 43 of their papers we have counts for
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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…
Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators
Vishvesh Kumar, Berikbol T. Torebek
The main goal of this paper is to establish \emph{necessary and sufficient conditions} for the nonexistence of a global solution to the semilinear heat equation with a mixed local-…
Fractional Morrey-Sobolev type embeddings and nonlocal subelliptic problems with oscillating nonlinearities on stratified Lie groups
Sekhar Ghosh, Tianxiang Gou, Vishvesh Kumar +1
In this paper, we establish the fractional Morrey-Sobolev type embeddings on stratified Lie groups. This extends and complements the Sobolev type embeddings derived in \cite{GKR}.…
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…
Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
Vishvesh Kumar, Shyam Swarup Mondal, Iswarya Sitiraju +1
In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that…
Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar
This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We esta…