Keywords: Benjamin–Bona–Mahony equation Method of compactness Moving boundary Crank–Nicolson method a b s t r a c t In this work we present the existence, the uniqueness and numerical solutions for a mathematical model associated with equations of Benjamin–Bona–Mahony type in a domain with moving boundary. We apply the Galerkin method, multiplier techniques, energy estimates and compactness res...

We investigate the semigroup structure of bosonic Gaussian quantum channels. Particular focus lies on the sets of channels which are divisible, idempotent or Markovian (in the sense of either belonging to one-parameter semigroups or being infinitesimal divisible). We show that the non-compactness of the set of Gaussian channels allows for remarkable differences when comparing the semigroup stru...

Products of integral-type and composition operators has been recently introduced by Li and Stević and studied in a series of their papers. In this note we study the boundedness and compactness of these products from generally weighted Bloch space to F (p, q, s) space, where 0 < p, s < ∞, q > −2, α > 0.

Under generic assumptions, we prove boundedness of Palais-Smale sequences relative to some geometric functional defined on H(M), where M is a four-dimensional manifold. Our analysis is useful to find critical points (via minimax arguments) of this functional, which give rise to conformal metrics of constant Q-curvature. The proof is based on a refined bubbling analysis, for which the main estim...

Let X be a real Banach space and Φ ∈ C 1 (X, R) a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence {u n } of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of u n from S for certain types of set S as n → ∞. Under our hypotheses we can ...

The main purpose of this paper is to establish a three critical points result without assuming the coercivity of the involved functional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then applied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions.

where Ω ⊂ R is a smooth domain with smooth boundary ∂Ω such that 0 Î Ω, Δpu = div(|∇u|∇u), 1 < p < N, μ < μ̄ = ( N−p p ), l >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on ̄, μ̄ = ( N−p p ) p is the best Hardy constant and p∗ = Np N−p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solu...

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between ...