The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted phi-Laplacian operator and subjected to Dirichlet boundary conditions. We also examine the presence of sequences of variational eigenvalues in two distinct scenarios, one with and one without assuming the Delta(2)-condition. Our main results are obtained through technical proofs that combine a Lagrange multipliers type approach with the Ljusternik-Schnirelmann argument.
In this paper, we not only show that the weak homogeneous Sobolev space W-.(alpha,p,infinity ) interpolates W-center dot(alpha,p) and BM(.)O(alpha,)but also propose the (BV, W-.a,W-p,W-infinity)-based model for image decomposition, thereby validating the interpolation inequality.
In this paper, we prove the existence of nontrivial solutions and multiple solutions for a specific class of p(x)-biharmonic system with Hardy potential and indefinite weight. Our major techniques incorporated variational approaches and several critical point theorems.
This paper is devoted to an intensive investigation of the major geometric aspects of the so-called (1, infinity) is not an element of p-harmonic capacitances within mathematical physics living on the Euclidean space & Ropf;(n >= 2).
The problem of decentralized guaranteed cost control for fractional-order interconnected time delay systems is considered in this paper. The design of guaranteed cost controllers is first proposed based on mathematical transformations with fractional calculus. A new sufficient condition in terms of linear matrix inequalities for the existence of decentralized guaranteed cost control for the interconnected fractional-order systems is derived. An example is provided to validate the correctness of the obtained theoretical results. Although there are some interesting methods for the design of guaranteed cost control laws for large-scale systems with integer order, they cannot be applied directly to fractional-order large-scale systems with time delays, since the Leibniz rule is not satisfied for fractional-order differentiation. Thus, designing a decentralized guaranteed cost control for fractional-order large-scale systems with time delays has been an open problem. The fractional-order Razumikhin theorem and mathematical transformations have been used to solve the decentralized guaranteed cost control for interconnected fractional-order systems with time-varying delays. The advantage of our approach is that it not only ensures that the controlled large-scale systems are asymptotically stable, but it also guarantees an adequate level of performance.
The article establishes the existence of a weak solution u is an element of W-1,0(p(& centerdot;)) (Omega), Omega subset of R-n, n > 2 to the operator equation A(lambda)(p(& centerdot;)) (u) = phi for each fixed phi is an element of W-1,0(p(& centerdot;)), where the operator A(lambda)(p(& centerdot;)) : W-1,0(p(& centerdot;)) -> W-1,0(p(& centerdot;)) is generated by the equation with the exponential p (center dot)-Laplacian equation (-del (|del u|(p(x)-2)del u) + a|u|(p(x)-2) u = lambda b (x) |u|(sigma(x)-2)u for b is an element of L p*(& centerdot;)/p*(& centerdot;)-sigma(& centerdot;) (Omega), p, sigma is an element of P-log (Omega) p* (x) = np(x)/n-p(x) , lambda >= 0 and 1 < sigma(m) <= sigma(S) < p(m) <= p(S) < infinity.
This paper considers the finite-time stability problem for conformable fractional-order time-delay nonlinear interconnected systems. Different from the existing methods in the literature dealing with the finite-time stability problem for conformable linear fractional-order systems without time delays, where the linear matrix inequality techniques are utilized, the one in this paper is based on the Gronwall-type conformable fractional inequality to solve this problem for conformable fractional-order time-delay nonlinear interconnected systems. A new delay-dependent sufficient condition is derived for the robust finite-time stability of the systems. The results are applied to the conformable fractional-order neural networks subject to time delays. Finally, the effectiveness of the obtained results is demonstrated by two numerical examples.
In this study, we explore multiplicity results for double-phase Kirchhoff problems characterized by singular nonlinearity. Using the Nehari manifold method and fibering map analysis, we demonstrate the existence of non-negative solutions to these problems.
Images are recognised as the most readily accessible and visually attractive means of digital communication. Most current multiple RGB image encryption techniques are specifically developed to encrypt photos of identical dimensions, resulting in a significant computational burden as compared to encrypting images of random size. The aim of this study is to introduce a new encryption technique for multiple RGB photos, which can encrypt multiple RGB images of different sizes while maintaining a higher level of security and speed than existing methods. The present study introduces a strategy called multiple RGB image encryption (MRG-BiE), which enables secure and efficient sharing of numerous RGB images using a single cipher. In order to produce and distribute the key, the Elliptic Curve (EC), Secure Hash Algorithm 256 (SHA-256), and the Diffie-Hellman Key (DHK) mechanism are employed. A hyper-chaotic system is used to make sure that the results are random, along with operations like XOR, point multiplication over EC, QR decomposition, and image scrambling using a hash value-dependent key. The experimental findings demonstrate that the MRGBiE scheme is efficient, robust to various attacks, and significantly faster as compared to existing schemes.
This paper presents a viable methodology, named Complex Proportional Assessment, for addressing multi-criteria group decision making issues in the symmetric octagonal fuzzy number. To start with, the concept of arithmetic operations, average aggregation operators, and a robust ranking technique of symmetric octagonal fuzzy numbers are introduced. When dealing with uncertainty, symmetric octagonal fuzzy numbers are a better option than other generalized fuzzy numbers. The Complex Proportional Assessment algorithm is developed using group decision making within the context of the suggested symmetric octagonal fuzzy numbers. The proposed approach includes a powerful computational mechanism that manages the decision maker's level of satisfaction with their assessment. In order to validate the developed decision-making approach in the symmetric octagonal fuzzy environment, numerical examples appear, and both the selection process of renewable energy projects and the software systems are taken into consideration.
In this paper, we consider a vector-valued control problem where the objective function takes its values in a linear space. We characterize (weakly, properly) efficient solutions of the vector-valued control problem using the nonlinear scalarization function due to Gerstewitz which is defined on the linear image space of the objective function.
Let (X, rho, mu) be a space of homogeneous type in the sense of Coif-man and Weiss, and let D=(boolean OR k is an element of)ZD(k) be a system of dyadic cubeson X. For any f is an element of L-p(X) with p is an element of(1,infinity), let E-k(f) be the conditional expectation off on Dk and let Ek(f)=Ek+1(f)-Ek(f) be the martingale difference. In this article, we will establish a good-lambda inequality associated to a new dyadic square function S(f)(x)=(Sigma k is an element of Z|Ek(f)(x)|2)1/2that there exist constantsC1,C2>0 and sufficiently small gamma>0, such that for any lambda>0, mu({x is an element of X:(f-fX)*(x)>2 lambda, S(f)(x)<=gamma lambda}) <= C(1)exp(-C-2(/)gamma(2))mu({x is an element of X:(f-fX)*(x)>lambda}), where f*(x)=sup(k)|E-k(f)(x)|,fX=mu(X)(-1)integral Xf(x)d mu(x) for mu(X)
The main purpose of this paper is to construct compact Lagrangian submanifolds satisfying Maslov's quantization condition in the cotangent bundle of the Cayley projective plane by making use of the explicit realization of its punctured cotangent bundle as a quadric in the complex space & Copf;(27){0}. If the geodesic flow is completely integrable, then there are many Lagrangian submanifolds, all of which are tori. Our examples are not tori. For this purpose we explain Maslov class based on our earlier work on the Maslov index defined for arbitrary paths for the sake of the self-containedness, and based on this treatment of the Maslov index we determine the Lagrangian submanifolds satisfying Maslov's quantization condition.
This note offers a capacity analysis of the fractional heat kernel induced potential u(t, x)=e(-t)(-Delta(x))(alpha)f(x) subject to both f is an element of L(1,0
Nonlinear conjugate gradient methods offer an efficient framework for solving multiobjective optimization problems without initially reducing the objective function to a scalar form. Several extensions of nonlinear conjugate gradient methods, such as the Polak-Ribi & eacute;re-Polyak (PRP) and hybrid nonlinear conjugate gradient methods have been studied in the literature and extended to multiobjective optimization. However, the analysis of these methods often reveals that their search directions either lack descent properties or rely heavily on line search techniques to maintain such properties. In this paper, we propose two novel three-term-like nonlinear conjugate gradient methods for multiobjective optimization problems. The first method incorporates the PRP nonlinear conjugate gradient method, while the second adopts a hybrid strategy that selects the maximum between zero and the minimum of the PRP and Dai-Yuan conjugate parameters. In particular, the proposed methods ensure the sufficient descent condition automatically, without requiring any line search techniques. We establish the global convergence of the proposed methods using the standard Wolfe line search. Numerical experiments on benchmark problems from the literature demonstrate the efficiency, robustness, and performance of the methods in terms of purity and spread metrics.
In this paper, we study a generalized vector-valued approximation problem that involves a not necessarily convex feasible set, and the objective function is acting between Banach spaces. By applying the known notions of generalized differentiation and some moderate assumptions concerning the vector-valued objective function, feasible set, and the involved ordering cone in the image space, we derive necessary optimality conditions for weakly efficient solutions of the vector-valued approximation problem. Because the set of efficient solutions may be very large, we are trying to find an element belonging to it that corresponds to the preferences of the decision maker. This will be done using the well-known nonlinear Gerstewitz scalarizing functional where the involved parameters describe the preferences of the decision maker. We consider an associated scalar problem over the set of efficient solutions to the vector-valued approximation problem and the corresponding optimality condition for the associated scalar problem. In addition, we apply our results for the special case of multiobjective location problems. Using the known primal-dual algorithm for generating the whole set of efficient solutions, we generate solutions corresponding to the preferences of the decision maker.
In this paper, we study the optimal control problem of a class of space-time fractional parabolic-elliptic Keller-Segel equations with logistic source terms in R-n, n >= 2. We first prove the existence and uniqueness of the weak solution. Then, we obtain the existence of the optimal control under some conditions.
This paper is about an optimal stock selling rule with trading constraints. The goal is determining the time to sell the equity to maximize a discounted reward function. A geometric Brownian motion model represents the underlying stock price movement, and the trading permission process is given in terms of a two-state Markov chain. The optimal policy is determined by a threshold level obtained from solving an associated set of Hamilton-Jacobi-Bellman (HJB) equations (quasi-variational inequalities), from which a closed-form solution is obtained. A verification theorem is provided. Numerical experiments are also included to demonstrate the dependence of the optimal policy and value functions on input parameters.
