4 papers
The best constant in the G-N inequality for the mixed local and Nonlocal Laplacian
Hichem Hajaiej, Yu Su
In this paper, we establish the best constant in the G-N inequality for the mixed local and nonlocal Laplacian. In our problem, classical methods cannot apply directly since regula…
Mixed-dispersion Schrödinger equations and Gagliardo-Nirenberg inequalities: equivalence between ground states and optimizers
Zhisu Liu, Giulio Romani, Yu Su
We study a nonlinear Schrödinger equation with mixed dispersion in the mass competition regime, namely mass-supercritical for the Laplacian and mass-subcritical for the Bilaplacia…
Explicit Formula Of The Critical Mass And The Energy Ground State Solution For The Mixed Local-Nonlocal Schrodinger Equation For The In-Between Critical Exponents Case
Yu Su, Hichem Hajaiej
Our first main contribution consists in establishing an explicit formula of the critical mass via the best constant of the Gagliardo-Nirenberg inequality for the mixed local-nonloc…
Ground State Solutions For Local-Nonlocal Shrodinger Equations In the Presence Of Two Critical Exponents
Yu Su, Hichem Hajaiej, Hongxia Shi
In this paper, we address the existence of ground state solutions for Schrodinger equations in the presence of local and nonlocal operators and two critical nonlinearities associat…