Based on recent developments in the theory of fractional Sobolev spaces, an interesting new class nonlocal variational problems has emerged literature. These problems, which are focus this work, involve integral functionals that depend Riesz gradients instead ordinary and considered subject to a complementary-value condition. With goal establishing comprehensive existence theory, we provide ful...

In this paper, the relationships between semicontinuity and preinvexity of fuzzy mappings are investigated. The concepts of intermediate-point preinvex fuzzy mappings and weakly preinvex fuzzy mappings are first introduced, and the authors establish a characterization for a weakly preinvex fuzzy mapping in terms of its epigraph. In this context, a characterization of a preinvex fuzzy mapping in...

We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove lower semicontinuity smooth varieties if exponent an ideal is less than canonical threshold ideal.

4 The Dwork-Robba theorem and the upper semicontinuity of ξ 7→ R(ξ,Σ) 9 4.1 The global growth estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 The generalized Dwork-Robba theorem . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Upper semicontinuity of ξ 7→ R(ξ,Σ) . . . . . . . . . . . . . . . . . . . . . . . 13 4.4 Continuity of ξ 7→ R(ξ,Σ) at maximal points (Dwork’s tra...

The (PS)-weak lower semicontinuity property has been introduced in Vasiliu and Yan [10] for general continuously differentiable functionals on Sobolev spaces in connection with the Ekeland variational principle and the direct method of calculus of variations. In this paper, we give a necessary and sufficient condition of this property for the functionals in one-dimension of the simple type I(u)...

The well-known Caristi fixed point theorem has numerous generalizations and modifications. Recently there
 have appeared its equivalent dual forms based on new concept of lower semicontinuity
 from above by several authors. In the present article, we give proofs such versions their
 formulations applying our Metatheorem in ordered theory.

By considering the new forms of notions lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity considered scalar multiple integral functional, in this paper we study well-posedness a class variational problems with inequality constraints. More specifically, by defining set approximating solutions for under study, establish several results on well-posedness.

In 1997, Macal and Hurter [7] have found that adding a constraint to the lower level problem, which is not active at the computed global optimal solution, can destroy global optimality. In this paper this property is reconsidered and it is shown that this solution remains locally optimal under inner semicontinuity of the original solution set mapping. In the second part of the paper we prove th...