In the paper, we gave a strengthening of our previous work in \cite{Li1} (J. Differ. Equ. 269 (2020)) and proved that data-to-solution map for Camassa-Holm equation is nowhere uniformly continuous $B^s_{p,r}(\R)$ with $s>\max\{1+1/{p},3/2\}$ $(p,r)\in [1,\infty]\times[1,\infty)$. The method applies also to b-family equations which contain Degasperis-Procesi equations.

This paper outlines a way for thinking about continuity and change in childhood anxiety symptoms. Considerations for a model of continuity and change in anxious emotion are discussed first. Then, a perspective which may resolve inconsistencies across studies on the stability of childhood anxiety problems overtime is presented. The perspective views dysregulation of the anxiety response system a...

In this paper we study weak continuity of the dynamical systems for the KdV equation in H−3/4(R) and the modified KdV equation in H1/4(R). This topic should have significant applications in the study of other properties of these equations such as finite time blow-up and asymptotic stability and instability of solitary waves. The spaces considered here are borderline Sobolev spaces for the corre...

The FETI method is based on introducing Lagrange multipliers along interfaces between subdomain to enforce continuity of local solutions [4]. It has been demonstrated to be numerically scalable in the case of second-order problems, thanks to a built-in “coarse grid” projection [3]. For high-order problems, especially with plate or shell finite element models in structural analysis, a two-level ...

We prove necessary and sufficient conditions for the validity of Jensen type inequalities for generalized Sugeno integral. Our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators. For several choices of operators, we characterize the classes of functions for which the corresponding inequalities are satisfied.

We study equilibrium problems with strongly pseudomonotone bifunctions in real Hilbert spaces. We show the existence of a unique solution. We then propose a generalized strongly convergent projection method for equilibrium problems with strongly pseudomonotone bifunctions. The proposed method uses only one projection without requiring Lipschitz continuity. Application to variational inequalitie...

The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche’s stability condition. The entropies of Tsallis’ nonextensive thermostatistics are taken as exam...

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.