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The aim of the present paper is to state and discuss the well-posedness of a new evolution inclusion governed by the subdifferential of a function φ perturbed both by a Carathéodory mapping and by an integral forcing term. The integrand of the forcing term depends on two time-variables. We prove the existence and uniqueness of local and global solution, assuming that φ is primal lower regular and the perturbation terms satisfy some standard conditions. The results are applied to the study of non-regular electrical circuits with tranmission line, Zener diode and inductor. A second application is concerned with semilinear heat equation with memory. These applications illustrate an additional novelty of our paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the approximate controllability for Hilfer fractional stochastic hemivariational inequalities of order 1 < μ < 2 in Hilbert spaces. Initially, we define the concept of a mild solution for our problem in terms of fractional calculus, cosine families, stochastic analysis, and generalized Clarke subdifferential. Then, the existence and approximate controllability for Hilfer fractional stochastic evolution hemivariational inequalities are formulated and proven under appropriate conditions using fixed point theorems for multivalued maps. Finally, an example is presented to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with two multivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixed point principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existence theorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and give sufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of the theoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone and multivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundary condition, a unilateral contact condition of Signorini's type and an implicit obstacle effect, in which the multivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundary condition is formulated by the convex subdifferential operator for a convex superpotential. [ABSTRACT FROM AUTHOR]

In this paper, for d ≥ 1 and s ∈ (0 , d 2) , we study the Bianchi–Egnell quotient Q (f) = inf f ∈ H ˙ s (R d) \ B ‖ (- Δ) s / 2 f ‖ L 2 (R d) 2 - S d , s ‖ f ‖ L 2 d d - 2 s (R d) 2 dist H ˙ s (R d) (f , B) 2 , f ∈ H ˙ s (R d) \ B , where S d , s is the best Sobolev constant and B is the manifold of Sobolev optimizers. By a fine asymptotic analysis, we prove that when d = 1 , there is a neighborhood of B on which the quotient Q (f) is larger than the lowest value attainable by sequences converging to B . This behavior is surprising because it is contrary to the situation in dimension d ≥ 2 described recently in König (Bull Lond Math Soc 55(4):2070–2075, 2023). This leads us to conjecture that for d = 1 , Q (f) has no minimizer on H ˙ s (R d) \ B , which again would be contrary to the situation in d ≥ 2 . As a complement of the above, we study a family of test functions which interpolates between one and two Talenti bubbles, for every d ≥ 1 . For d ≥ 2 , this family yields an alternative proof of the main result of König (Bull Lond Math Soc 55(4):2070–2075, 2023). For d = 1 we make some numerical observations which support the conjecture stated above. [ABSTRACT FROM AUTHOR]

This paper proposes, in the framework of Hadamard manifolds, two iterative schemes for approximating a solution of a variational inequality problem involving a nonexpansive mapping with a fixed point set of another nonexpansive mapping as constraint. The first scheme is a modified Halpern iteration and the second is a viscosity-type iteration with a weakly contraction mapping. We also discuss some special cases of the mentioned problem. Numerical examples are provided to illustrate the algorithm's numerical behavior. [ABSTRACT FROM AUTHOR]