S.C.-Y. Lu
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View article: Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation
Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation Open
In any dimension [Formula: see text], for given mass [Formula: see text] and when the [Formula: see text] energy functional [Formula: see text] is coercive on the mass constraint [Formula: see text] we are interested in searching for const…
View article: Normalized solutions with positive energies for a coercive problem and\n application to the cubic-quintic nonlinear Schr\\"{o}dinger equation
Normalized solutions with positive energies for a coercive problem and\n application to the cubic-quintic nonlinear Schr\\"{o}dinger equation Open
In any dimension $N \\geq 1$, for given mass $m > 0$ and when the $C^1$ energy\nfunctional\n \\begin{equation*}\n I(u) := \\frac{1}{2} \\int_{\\mathbb{R}^N} |\\nabla u|^2 dx - \\int_{\\mathbb{R}^N}\nF(u) dx\n \\end{equation*}\n is coercive…
View article: Nonradial normalized solutions for nonlinear scalar field equations
Nonradial normalized solutions for nonlinear scalar field equations Open
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\m…
View article: Variational methods for degenerate Kirchhoff equations
Variational methods for degenerate Kirchhoff equations Open
For a degenerate autonomous Kirchhoff equation which is set on $\mathbb{R}^N$ and involves the Berestycki-Lions type nonlinearity, we cope with the cases $N=2,3$ and $N\geq5$ by using mountain pass and symmetric mountain pass approaches an…
View article: Multiple solutions for a Kirchhoff-type equation with general nonlinearity
Multiple solutions for a Kirchhoff-type equation with general nonlinearity Open
This paper is devoted to the study of the following autonomous Kirchhoff-type equation: - M ( ∫ ℝ N | ∇ u | 2 ) Δ u = f ( u ) , u ∈ H 1 ( ℝ N ) , -M\biggl{(}\int_{\mathbb{R}^{N}}|\nabla{u…