General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established. The dependence of solution uniqueness classes of the first boundary value problem for a second-order parabolic equation in an unbounded domain on the domain...

We consider the analytic continuation of the transfer function associated with a 2×2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which factorize the transfer function and reproduce certain parts of its spectrum including the nonreal (resonance) spectrum situated in the unphysical sheets neighboring ...

We will show that under suitable conditions on f and h, there exists a positive number λ∗ such that the nonhomogeneous elliptic equation −Δu + u = λ( f (x,u) + h(x)) in Ω, u ∈ H 0 (Ω), N ≥ 2, has at least two positive solutions if λ ∈ (0,λ∗), a unique positive solution if λ = λ∗ , and no positive solution if λ > λ∗ , where Ω is the entire space or an exterior domain or an unbounded cylinder dom...

In this paper, we investigate a nonlocal periodic reaction-diffusion population model with stage structure. In the case of unbounded spatial domain, we establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone periodic traveling waves. In the case of bounded spatial domain, we obtain a threshold result on the global attractivit...

We propose a novel class of arbitrarily high-order mass or energy conservative numerical schemes for the generalized Benjamin–Ono equation on whole real line. The spatial discretization is achieved by pseudo-spectral method with rational basis functions. By reformulating discretized system into different equivalent forms, either semi-discretized can be preserved exactly under continuous time fl...