The paper is concerned with the local and global bifurcation structure of positive solutions u,
v ∈ H^ 1_0 (Ω) of the system\left {-Δ u+ u=\mu_1u^ 3+ β v^ 2u &\quad in Ω\-Δ v+ v=\mu_2v …

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 …

In this paper we study the following coupled Schrödinger system, which can be seen as a
critically coupled perturbed Brezis–Nirenberg problem:\left {-Δ u+\lambda_1 u=\mu_1 u^ 3+ …

We consider the nonlinear elliptic system\left {-& Δ u+ uu^ 3-β v^ 2u= 0\quad in\,\mathbb B,\-
& Δ v+ vv^ 3-β u^ 2v= 0\quad in\,\mathbb B,\&u, v> 0\quad in\,\mathbb B,\quad u= v= 0\quad …

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 study the following nonlinear Schrödinger system which is related to Bose–Einstein
condensate:{.-Δ u+ λ 1 u= μ 1 u 2∗-1+ β u 2∗ 2-1 v 2∗ 2, x∈ Ω,-Δ v+ λ 2 v= μ 2 v 2∗-1+ β v …

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 consider the following k-coupled nonlinear Schrödinger systems:{− Δ u j+ λ juj= μ juj
3+∑ i= 1, i≠ jk β i, jui 2 uj in RN, uj> 0 in RN, uj (x)→ 0 as| x|→+∞, j= 1, 2,⋯, k, where N≤ 3 …

A diffusive Lotka–Volterra competition model with nonlocal intraspecific and interspecific
competition between species is formulated and analyzed. The nonlocal competition strength …

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