55 citations · 120 across the 12 of their papers we have counts for
12 papers
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,…
On fractional Schrödinger equations with Hartree type nonlinearities
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
Goal of this paper is to study the following doubly nonlocal equation \begin{equation}\label{eq_abstract} (- Δ)^s u + μu = (I_α*F(u))F'(u) \quad \hbox{in } \tag{P} \e…
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
We study existence of solutions for the fractional problem \begin{equation*} (P_m) \quad \left \{ \begin{aligned} (-Δ)^{s} u + μu &=g(u) & \; \text{in }, \cr \int_{\m…
A note on deformation argument for constraint problem
Norihisa Ikoma, Kazunaga Tanaka
We study the existence of normalized solutions for nonlinear Schrödinger equations and systems. Under new Palais-Smale type conditions we develop new deformation arguments fo…
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}\…
Remarks on the Clark theorem
Guosheng Jiang, Kazunaga Tanaka, Chengxiang Zhang
The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to and…
Multi-bump solutions for logarithmic Schrödinger equations
Kazunaga Tanaka, Chengxiang Zhang
We study spatially periodic logarithmic Schrödinger equations: \begin{equation}\tag{LS} -Δu + V(x)u=Q(x)u\log u^2, \quad u>0\quad \text{in}\ \mathbb{R}^N, \end{equation} where $N\g…
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}…
Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions
David Arcoya, Colette De Coster, Louis Jeanjean +1
In this note we present some uniqueness and comparison results for a class of problem of the form \begin{equation} \label{EE0} \begin{array}{c} - L u = H(x,u,\nabla u)+ h(x), \quad…
Multiplicity of positive solutions of nonlinear Schrödinger équations concentrating at a potential well
Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka
We consider singularly perturbed nonlinear Schrödinger equations \be \label{eq:0.1} - \varepsilon^2 Δu + V(x)u = f(u), \ \ u > 0, \ \ v \in H^1(\R^N) \ee where …
Continuum of solutions for an elliptic problem with critical growth in the gradient
David Arcoya, Colette De Coster, Louis Jeanjean +1
We consider the boundary value problem \begin{equation*} - Δu = λc(x)u+ μ(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(Ω) \cap L^{\infty}(Ω) \eqno{(P_λ)} \end{equation*} where $Ω\subs…