8 citations · 11 across the 6 of their papers we have counts for
6 papers
Sharp homogeneous Gagliardo--Nirenberg inequalities and normalized solutions for generalized stationary MMT equations
Amin Esfahani, Mukhtar Karazym
We prove the existence of optimizers for a class of homogeneous Gagliardo-Nirenberg inequalities of the form $$ \|D^{s}ϕ\|_{L^q} \leq C \|D^{s_1}ϕ\|_{L^p}^{1-θ} \|D^{s_2}ϕ\|_{L^2}^…
Traveling Waves for Nonlocal Derivative Nonlinear Schrödinger Equations: A Variational Characterization
Amin Esfahani, Adilbek Kairzhan, Mukhtar Karazym
We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger equation with general coefficients by variational methods. We s…
Variational eigenvalues of the subelliptic -Laplacian
Mukhtar Karazym
We use the Lusternik-Schnirelman theory to prove the existence of a nondecreasing sequence of variational eigenvalues for the subelliptic -Laplacian subject to the Dirichlet bou…
Subelliptic -Laplacian spectral problem for Hörmander vector fields
Mukhtar Karazym, Durvudkhan Suragan
Based on variational methods, we study the spectral problem for the subelliptic -Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove…
Trace formulae of potentials for degenerate parabolic equations
Mukhtar Karazym, Durvudkhan Suragan
In this paper, we analyze main properties of the volume and layer potentials as well as the Poisson integral for a multi-dimensional degenerate parabolic equation. As consequences,…
Multidimensional inverse Cauchy problems for evolution equations
Mukhtar Karazym, Tohru Ozawa, Durvudkhan Suragan
We discuss inverse problems to finding the time-dependent coefficient for the multidimensional Cauchy problems for both strictly hyperbolic equations and polyharmonic heat equation…