4 papers · 1 filter
Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
In this paper we study the following nonlinear fractional Choquard-Pekar equation \begin{equation}\label{eq_abstract} (-Δ)^s u + μu =(I_α*F(u)) F'(u) \quad \hbox{in}\ \mathbb{R}^N,…
Nonlinear scalar field equations with constraint: Mountain pass and symmetric mountain pass approaches
Jun Hirata, Kazunaga Tanaka
We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in (): $$ (*)_m \left\{ \eqalign{ -&Δu = g(u) -μu…
Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well
Silvia Cingolani, Kazunaga Tanaka
We study existence and multiplicity of semi-classical states for the nonlinear Choquard equation: $$ -\varepsilon^2Δv+V(x)v = \frac{1}{\varepsilon^α}(I_α*F(v))f(v) \quad \hbox{in}\…
Multiple complex-valued solutions for nonlinear magnetic Schrodinger equations
Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka
We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations $$ L^{\hbar}_{A,V} u = f(|u|^2)u \quad \mbox{in } R^N $$ where , $L^{\hbar}…