For the positive solutions of the Gross–Pitaevskii system-Δ u_ β+ β u_ β= 1 u 3\over β-β u_ β
v 2\over β,\cr-Δ v_ β+ β v_ β= 2 v 3\over β-β u 2\over β v_ β, we prove that L∞‐boundedness …

We consider mainly the Dirichlet realization of the Laplacian operator in Ω, when Ω is a
bounded domain in R with piecewise-C boundary (domains with corners or cracks 10.1 …

For a class of population models of competitive type, we study the asymptotic behavior of the
positive solutions as the competition rate tends to infinity. We show that the limiting problem …

We discuss the effects of dispersal (either random or biased) and spatial heterogeneity on
population dynamics via reaction–advection–diffusion models. We address the question of …

We consider two-dimensional Schrödinger operators in bounded domains. We analyze
relations between the nodal domains of eigenfunctions, spectral minimal partitions and …

Here we study the asymptotic limits of solutions of some singularly perturbed elliptic
systems. The limiting problems involve multiple valued harmonic functions or, in general …

We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli
problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a …

Nonlinear functional analysis is an important branch of contemporary mathematics. It's
related to topology, ordinary differential equations, partial differential equations, groups …

We establish the limit system for the Gross–Pitaevskii equations when the segregation
phenomenon appears, and shows this limit is the one arising from the competing systems in …

For studying the evolution of the transverse deflection of an extensible beam derived from
the connection mechanics, we investigate the initial boundary value problem of nonlinear …