-valued maps minimizing the norm of the gradient with free discontinuities
Sätze des Khintchine Typus für Mengenfunktionen
Schauder bases in an abstract setting.
Second order differentiability and Lipschitz smooth points of convex functionals
Second order linear -difference equations: nonoscillation and asymptotics
The paper can be understood as a completion of the -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear -difference equations. The -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice with . In addition to recalling the existing concepts of -regular variation and -rapid variation we introduce -regularly bounded functions and prove many related properties. The -Karamata theory is then...
Self-adjoint differential equations and generalized Karamata functions
Selfadjoint Means and Operator Monotone Functions.
Semiéquicontinuité approximative et measurabilité
Semigroups of ...-density continuous functions.
Semilinear fractional order integro-differential equations with infinite delay in Banach spaces
This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.
Semilinear functional differential equations of fractional order with state-dependent delay.
Separate approximate continuity and strong approximate continuity
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Separation by monotonic functions.
Separation via quadratic functions.
Separation via quadratic functions. (Summary).
Series solutions of time-fractional PDEs by homotopy analysis method.
Set-valued fractional order differential equations in the space of summable functions
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type , a.e. on (0,1), , αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
We make some comments on the problem of how the Henstock-Kurzweil integral extends the McShane integral for vector-valued functions from the descriptive point of view.
Sharkovskiĭ's theorem holds for some discontinuous functions
We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected graph.