This paper is concernedwith a periodic system dependent on parameter. We study differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for C0-semigroups, we obtained some convenient conditions for determining differentiability with parameters of the periodic solution. The paper is concluded with an ...

Abstract. Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. S...

The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case. Namely, convex functions are always considered to be defined on convex sets with nonempty interior. But typically, ...

This paper focuses on the differentiability properties of the control-to-state mapping for entropy solutions to a scalar hyperbolic conservation law on R with respect to the switching times of an on/off control. As an example we consider the traffic density on a unidirectional road described by the LWR-model that is controlled by a traffic light switching between red and green at certain times....

We are concerned with the multiplicity of positive solutions for singular superlinear and subcritical Schrödinger equation [Formula: see text] beyond Nehari extremal value, as defined in [Y. Il’yasov, On extreme values manifold via nonlinear Rayleigh’s quotient, Topol. Methods Nonlinear Anal. 49 (2017) 683–714], when potential may change its sign, text], is a continuous function, real parameter...