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math.AP2026
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}^…
math.AP2026
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…