Related papers: A general variational principle and some of its ap…
The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss…
We consider locally equi-continuous strongly continuous semigroups on locally convex spaces (X,tau). First, we show that if (X,tau) has the property that weak* compact sets of the dual are equi-continuous, then strong continuity of the…
In classical analysis, the relationship between continuity and Riemann integrability is an intimate one: a continuous function on a closed and bounded interval is always Riemann integrable whereas a Riemann integrable function is continuous…
The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space $X$ with a basis. (i) $X$ is finite-dimensional if and only if every bounded, uniformly continuous, mean…
We study a logarithmic fractional Schr\"odinger--Poisson system in \(\R^{3}\): \begin{equation*} \begin{cases} \varepsilon^{2\alpha}(-\Delta)^{\alpha}u+V(x)u+\phi u=u\log u^{2}+|u|^{p-2}u, & \text{in }\R^{3},\\…
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…
We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley $g$-function for semigroups acting on $L^p$-spaces of functions with values in…
We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is…
The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity.…
First we prove that if a separable Banach space $X$ contains an isometric copy of an infinite-dimensional space $A(S)$ of affine continuous functions on a Choquet simplex $S$, then its dual $X^*$ lacks the weak$^*$ fixed point property for…
We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient and which is related to the minimization of the nonlocal…
A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method,…
In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…
A Banach space $X$ has \textit{property $(K)$}, whenever every weak* null sequence in the dual space admits a convex block subsequence $(f_{n})_{n=1}^\infty$ so that $\langle f_{n},x_{n}\rangle\to 0$ as $n\to \infty$ for every weakly null…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
Without compactness assumptions, we prove some abstract results which show that a $C^{1}$ functional $I:X\rightarrow \mathbb{R}$ on a Banach space $X$ admits bounded Palais-Smale sequences provided that it exhibits some geometric structure…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
A finite-dimensional analogue of the known Gordon-Lewis constant of a Banach space X is introduced; in its definition are used only finite rank operators. It is shown that there exist Banach spaces such that the standard Gordon-Lewis…