We investigate weak solutions of a quasilinear (p, p)-biharmonic sys-tem with variational structure. Using the principal eigenvalue of the associated system and the linking theorem of Brezis and Nirenberg, we establish the existence of at least two nontrivial weak solutions for the eigenvalue parameter λ in a closed right neighborhood of zero. Our results apply in both resonant and nonresonant cases, depending on the asymptotic behavior of the nonlinear term. These findings extend earlier work on scalar biharmonic equations and systems, and cover several important special cases arising from different choices of the coefficients.

We introduce the notion of α-ψ-R contractive mappings that act on a metric space. We establish the existence and uniqueness of fixed points for this class of mappings and provide a sequence of iterates which approximate their fixed points. Some examples are presented and the relationships with some previous results are described.

We investigate the existence of generalized solutions to a non-coercive competing system driven by the (p, q)-Laplacian. In order to reach the existence result, we derive an abstract principle based on the convergence of the Galerkin scheme.

In this paper, we propose the concept of ρ-strong convergence for difference sequences of fractional order, denoted by ∆α-ρ-strong con vergence, in a q-rung orthopair fuzzy normed space. We establish the uniqueness of this convergence and provide its algebraic characteriza tion. A convergence criterion for subsequences is derived, and the rela tionship between ∆α-strong convergence and ∆α-ρ-strong convergence is examined under conditions on liminf s ρs . Moreover, an inclusion re sult is obtained by employing a positive non-decreasing sequence µs satisfying ρs µs under suitable assumptions. Finally, we introduce the notion of ρ-strongly Cauchy difference sequences of fractional order and investigate their connection with ∆α-ρ-strong convergence.

A Steiner triple system (STS) of order v is a 3-uniform hypergraph with v vertices in which every 2-subset of vertices has degree 1. A Kirkman triple system (KTS) is a resolvable Steiner triple system, that is, a partition of the blocks of the triple system into classes which are themselves partitions of the set of vertices into disjoint blocks. In this paper we give a construction of KTS of order v = 3h much simpler and less technical than previously known constructions.

This paper investigates exact detectability of systems with periodic coefficients in finite-dimensional real ordered Hilbert spaces, extending the classical framework of positive systems, which have applications in many fields. A spectral PBH-type criterion for detectability is established for both discrete and continuous-time systems in a unified treatment. We further propose a Barbasin–Krasovskii-type criterion for exponential stability by showing that the existence of a solution to a dual system, combined with detectability, ensures stability. The obtained results provide a Lyapunov-like framework and open directions for studying stability in optimal control.

In this paper, we first present a sensitivity analysis for extended real-valued hemivariational inequalities and variational–hemivariational inequalities in reflexive Banach spaces. In particular, we provide esti-mates of Lipschitz type with respect to parametric perturbations in the elliptic operator and the Clarke directional derivative. Then, we apply our quantitative stability result to an elliptic scalar boundary value problem that models unilateral contact problems in solid mechanics with nonmonotone friction.

We introduce some sequences approximating the constant e, related to the sequence defining the constant e and its irrationality. The main tool for constructing those sequences is a result of Ces`aro-Stolz type. Some related inequalities are given.

Let A and B be non-empty subsets of a metric space (X,d). Let T : A∪B → A∪B be a map such that T(A) ⊆ B and T(B) ⊆ A satisfying a certain contractive condition called cyclic orbital proximal contraction. We give the necessary conditions for the existence of a unique point ξ ∈ A such that d(ξ,Tξ) is equal to the distance between A and B. Our main result generalizes the main result of [A.A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006].

Consider in a real Hilbert space H, ( , ), the following in-complete Cauchy problem, (utt(t) = ∇φ(u(t)), t ≥ 0, (E) where u0 H is a given initial state, and φ : H R is a C1, non-convex function (preferably quasiconvex, as explained below). We call (ICP ) an incomplete Cauchy problem because the usual additional Cauchy condition ut(0) = v0 is missing. In this paper, we establish sufficient conditions on the non-convex function φ guaranteeing the existence of bounded solutions on [0, ∞) of (ICP ) for any u0 ∈ H.