This paper proposes a novel iterative method for addressing the split general system of variational inequalities and related fixed point problems within the framework of real Hilbert spaces. The algorithm is constructed by combining Halpern-type iterations with nonexpansive mappings, and its design guarantees strong convergence under appropriate conditions. The analytical results demonstrate that the proposed method not only unifies but also generalizes several classical schemes, including the split feasibility problem and the split variational inequality problem. To substantiate the theoretical findings, numerical experiments are provided, illustrating the robustness and efficiency of the algorithm in solving complex optimization and equilibrium problems.
Fractional-order neutral-type recurrent neural networks (FONTRNNs) hold promise for dynamic modeling, yet fixed neutral term order in existing studies restricts regulation flexibility. This paper proposes a four-neuron FONTRNN with independently tunable neutral term order. By decoupling the characteristic equation into trigonometric-variable linear systems, we derive explicit delay-dependent stability criteria and Hopf bifurcation points via Cramer's rule. Notably, an extended bifurcation framework is developed by treating the neutral term order as the bifurcation parameter, with critical values solved through implicit function curve intersection. Numerical simulations verify that reducing the derivative order consistently stabilizes the system, while adjusting the neutral term order enhances or weakens stability depending on parameter configurations.
In this paper, we define a new class of system of additive-quadratic functional equations on Banach algebras, which we call the system of i-mappings, where i is an element of {1, 2}. We introduce the notion of a i-F-homomorphism-derivations (abbreviated i-F-hom-ders), with i is an element of {1,2} : for i = 1, F is a linear homomorphism, and for i = 2, f is a quadratic homomorphism on Banach algebras. Finally, using a fixed-point method, we investigate Hyers-Ulam stability for the system of additive-quadratic functional equations and i-F-hom-ders, employing Gavruta-type, Rassias-type and JMRassias-type control functions on Banach algebras.
In this paper, we present a new second-order finite difference scheme for Riesz spacefractional Allen-Cahn equations. We use a modified Crank-Nicolson finite difference scheme with stabilized terms of third-order numerical accuracy for temporal discretization. The discrete maximum bound principle, the maximum-norm error estimates, and the discrete energy stability of the proposed scheme are discussed. It is demonstrated that the proposed scheme is maximum bound principle preserving and unconditionally energy-stable for any nonnegative stabilization parameter beta which satisfies 0 <= beta <= 1/4. As far as we know, the proposed fully implicit second-order scheme has never been proved to preserve the maximum bound principle before except the Allen-Cahn equation with beta = 1/12 and beta = 0. Finally, some numerical experiments are performed to verify the theoretical results.
This paper outlines multiple sufficient conditions for the existence of at least one generalized solution to a mixed boundary value problem for a complete Sturm-Liouville equation. Our method relies on variational techniques. We extend and enhance some recent results and also provide a specific example to illustrate an application.
This paper is concerned with a nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models with time delay. We prove the global nonexistence of the solutions. These results generalize and improve some earlier related results in the literature.
For the high-order finite element discretization system of three-dimensional elasticity problems, a local multigrid (LMG) method based on bisection grids is proposed. By decomposing the high-order finite element space into a "high-frequency" component and a linear element space, and leveraging the properties of bisection grids and interpolation operators, the stability of this space decomposition and the validity of the strong Cauchy-Schwarz inequality are proven. Consequently, the uniform convergence of the LMG algorithm is established. Numerical experiments are provided to verify the correctness of the theoretical results.
In this paper, we introduce a new class of generalized alpha-psi-Geraghty proximal contraction multimaps and establish best proximity point results for such mappings in the context of generalized metric spaces. Our results extend, generalize, and enhance those of related and relevant results in the literature.
This paper is devoted to the study of a two-dimensional Schro & uml;dinger equation with a general nonlinear term and a large forcing term. It is proved that the equation admits a Whitney smooth family of small amplitude quasi-periodic solutions which are partially hyperbolic for the given frequency vector (non-external parameters) and the large forcing term. Firstly, by introducing a symplectic change of coordinates, the Hamiltonian of the equation is transformed into a linear autonomous system plus higher order term perturbation (non-small perturbation), that is, the reducibility of the non-autonomous linear part is realized. Secondly, by introducing a symplectic change of coordinates, and action-angle variables, the Hamiltonian is transformed into a small perturbation of nonlinear integrable normal form that depends on angle variables. Then, by introducing a new symplectic change of coordinates, the Hamiltonian is transformed into a small perturbation of linear integrable normal form. Finally, the existence of invariant tori of the Hamiltonian system associated with the equation is proved by constructing an infinite-dimensional Kolmogorov-Arnold-Moser (KAM) theorem.
In this paper, the control systems governed by Riemann-Liouville fractional differential equations is introduced in Hilbert spaces. First, C1-alpha-mild solution to Riemann-Liouville fractional control system is introduced by means of fractional resolvents. Then by fractional calculus and fixed point theorem, some sufficient conditions are derived to ensure the exact null controllability of Riemann-Liouville fractional differential equations. Finally, an example is presented to illustrate our abstract results.
This paper investigates the use of a rectangular mixed finite element combined with variational discretization to solve elliptic optimization problems with integral constraints. The state and co-state variables are discretized by using the Q(k-1,k) & times; Q(k,k-1) - Q(k,k) mixed finite element. The control variable is obtained via a variational discretization technique. Under appropriate regularity assumptions, convergence and superconvergence results are rigorously derived by introducing some auxiliary variables and projection operators. Some examples are given to confirm the results of the theoretical analysis.
This paper investigates the existence of infinitely many homoclinic solutions for damped vibration systems involving the p-Laplacian. The systems under consideration are of the form d/dt(| u(t)|(p-2) u(t))+q(t)| u(t)|(p-2) u(t)+del V(t,u(t)) =0,t is an element of R, where p > 1, q is an element of C(R, R), and V is an element of C1(R & times; R-N,R). The potential V(t, u) is a combination of two functions where the associated energy functional is not continuously differentiable and fails to satisfy the Palais-Smale condition. By employing variational methods and the critical point theory, we establish the existence of infinitely many homoclinic solutions. Our results extend previous works on damped vibration systems, highlighting the impact of non-smooth energy functionals. The findings contribute to the understanding of the dynamical behavior of solutions to non-conservative systems modeled by the p-Laplacian.
This paper focuses on the Cauchy problem of the 2D incompressible Cahn-Hilliard-MHD equations. We construct the global well-posedness of strong solutions to the model without full viscosity, magnetic diffusion, and mobility.
Based on the Avery-Peterson fixed point theorem and Green's function, we establish the existence result of at least triple strictly nondecreasing positive solutions to a three-point boundary value problem of a fractional differential equations with out the concavity or convexity of the unknown function. An example is also provided to illustrate our main results.
The stochastic generalized Korteweg-de-Vries-Zakharov-Kuznetsov (GKDV-ZK) equation driven by multiplicative noise is considered in this paper. The stochastic GKDV-ZK equation is transformed into another GKDV-ZK equation with random variable coefficients (GKDV-ZKE-RVCs) by applying a proper transformation. Rational, elliptic, hyperbolic, and trigonometric solutions for GKDV-ZKE-RVCs were obtained. In addition, we present several figures to illustrate how multiplicative noise impacts the exact solutions of the stochastic GKDV-ZK equation.
This study investigates the multiplicity of solutions for a system of p-Laplacian fractional differential equations (FDEs) subjected to both instantaneous and non-instantaneous impulses. By employing a variant of Bonanno's local minimum theorem, we establish the existence of one or two solutions under appropriate algebraic conditions, including the classical Ambrosetti-Rabinowitz (AR) condition applied to the nonlinear term. Additionally, utilizing the critical point theorems proposed by Averna and Bonanno, we explore the existence of two and three solutions in a specific scenario of the system. The results contribute to a deeper understanding of the solution structure of impulsive FDEs and demonstrate the effectiveness of advanced variational techniques in addressing complex differential systems.
This paper is devoted to the analysis of an existence result of a solution, in a certain sense, to a coupled, nonlinear, and degenerate problem in the context of inhomogeneous anisotropic Orlicz-Sobolev spaces. We consider the case where the N-functions do not satisfy the Delta(2)-condition.
The Petryshyn's fixed point theorem is applied for the condensing maps with respect to Kuratowski measure of noncompactness satisfying a boundary condition. This paper extends this theorem by using a new boundary condition and the measure of noncompactness defined by the system of axioms.
In this paper, the existence and uniqueness of solutions to a class of boundary value problems with coupled nonlinear Caputo fractional q-difference systems are considered. The existence of solutions is obtained by using Schaefer's fixed-point theorem. The uniqueness of the solutions is achieved by using Banach contraction mapping principle, which supplements the existing literature. Two examples exhibit the feasibility of the theoretical results in applications.
The Mann algorithm has been extensively studied as one of the most fundamental iterative schemes designed to find a fixed point of an averaged operator. In this paper, we aim to develop a new parallel algorithm improving the Mann algorithm with double inertial extrapolations to find a common fixed point of a finite family of nonexpansive mappings. Our proposed algorithm allows iterations to be carried out simultaneously. We prove the weak convergence under suitable conditions, and we give an example in infinite-dimensional spaces. Finally, we apply our algorithm in the context of image restoration to deblur images without prior knowledge of the blurring operator.
