We study normalized solutions for the following Choquard equations with lower critical
exponent and a local perturbation -Δu+λu=γ(I_α∗|u|^αN+1)|u|^αN-1u+μ|u|^q …

In this paper we study the semiclassical limit for the singularly perturbed Choquard
equation− ε 2 Δ u+ V (x) u= ε μ− 3 (∫ R 3 Q (y) G (u (y))| x− y| μ dy) Q (x) g (u) in R 3, where …

We deal with symmetry properties for solutions of nonlocal equations of the type where
s∈(0, 1) and the operator (− Δ) s is the so-called fractional Laplacian. The study of this …

We consider the following nonlinear Choquard equation with Dirichlet boundary condition−
Δ u=(∫ Ω| u| 2 μ⁎| x− y| μ dy)| u| 2 μ⁎− 2 u+ λ f (u) in Ω, where Ω is a smooth bounded …

This paper is concerned with the properties of L 2-normalized minimizers of the Gross–
Pitaevskii (GP) functional for a two-dimensional Bose–Einstein condensate with attractive …

In 1959 Buchdahl [HA Buchdahl, General relativistic fluid spheres, Phys. Rev. 116 (1959)
1027–1034] obtained the inequality 2M/R⩽ 8/9 under the assumptions that the energy …

SIR infection age models with a very general class of nonlinear incidence rates f (S, J) are
investigated. We give a necessary and sufficient condition for global asymptotic stability of …

The paper is devoted to the question as to how “bad” the junior coefficients of elliptic and
parabolic equations may be in order that classical properties of their solutions (such as the …

We present a study of what may be called an intrinsic metric for a general regular Dirichlet
form. For such forms we then prove a Rademacher type theorem. For strongly local forms we …

We prove Strichartz estimates for the Schrödinger equation with an electromagnetic
potential, in dimension n⩾ 3. The decay and regularity assumptions on the potentials are …