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math.AP2022
Blowing-up solutions for a nonlocal Liouville type equation
Matteo Cozzi, Antonio J. Fernández
We consider the nonlocal Liouville type equation $$ (-Δ)^{\frac{1}{2}} u = \varepsilon κ(x) e^u, \quad u > 0, \quad \mbox{in } I, \qquad u = 0, \quad \mbox{in } \mathbb{R} \setminu…
math.AP2020★ 33 cited
Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation
Antonio J. Fernández, Louis Jeanjean, Rainer Mandel +1
We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the norm (the \textit{mass}) } is kept fixe…