Search

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation − div ( A ( x ) ∇ u ) + b ( x ) ⋅ ∇ u = f ( u ) in exterior domains in R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]

In this paper we prove that spectral synthesis holds for a variety on an Abelian group if spectral analysis holds on it and the residue ring of the annihilator of the variety is a Noether ring. This extends the fundamental result of M. Lefranc about spectral synthesis on finitely generated Abelian groups. [ABSTRACT FROM AUTHOR]

This paper addresses the properties of the C 0 -semigroup generated by the reparable system with finite repair time. In particular, it can be shown that the C 0 -semigroup is eventually differentiable and eventually compact, which is not true for the case when the repair time is infinite, as discussed in [9] and [11] . [ABSTRACT FROM AUTHOR]

This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem of the Camassa–Holm equation. We present a well-posedness result and a blow-up criterion of solutions in the inhomogeneous Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we provide an existence result of periodic solutions to planar systems having a repulsive singularity on both the axes. We require a nonresonance assumption, related to the spectrum of the periodic problem associated to the Steen's planar system which is isochronous (see [15]). As a particular case we obtain the existence of periodic solutions to a periodically perturbed Steen's planar system. [Copyright &y& Elsevier]