3 papers
math.AP2018
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 (): $$ (*)_m \left\{ \eqalign{ -&Δu = g(u) -μu…
math.AP2017
Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well
Silvia Cingolani, Kazunaga Tanaka
We study existence and multiplicity of semi-classical states for the nonlinear Choquard equation: $$ -\varepsilon^2Δv+V(x)v = \frac{1}{\varepsilon^α}(I_α*F(v))f(v) \quad \hbox{in}\…
math.AP2016
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}…