2 citations · 4 across the 10 of their papers we have counts for
16 papers
On an anisotropic double phase problem with singular and sign changing nonlinearity
Prashanta Garain, Tuhina Mukherjee
This article consists of study of anisotropic double phase problems with singular term and sign changing subcritical as well as critical nonlinearity. Seeking the help of well know…
Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In this article we study singular subelliptic -Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic $p…
On -eigenvalues of subelliptic operators on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In the article we study the Dirichlet -eigenvalue problem for subelliptic non-commutative operators on nilpotent Lie groups. We prove solvability of this eigenvalue problem…
On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
Prashanta Garain, Juha Kinnunen
We consider mixed local and nonlocal quasilinear parabolic equations of -Laplace type and discuss several regularity properties of weak solutions for such equations. More precis…
Multiple solutions for a class of quasilinear problems with double criticality
Karima Ait-Mahiout, Claudianor O. Alves, Prashanta Garain
We establish multiplicity results for the following class of quasilinear problems $$ \left\{ \begin{array}{l} -Δ_Φu=f(x,u) \quad \mbox{in} \quad Ω, \\ u=0 \quad \mbox{on} \quad \pa…
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems
Prashanta Garain, Alexander Ukhlov
In this article, we consider mixed local and nonlocal Sobolev -inequalities with extremal in the case . We prove that the extremal of such inequalities is un…