EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.

MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi｜u｜^p-2/｜x-ai｜p^u=｜u｜^p^＊-2u＋λ｜u｜^q-2u,x∈Ω,where Ω belong to R^N（N ≥ 3） is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=（N-p/p）^p,λ〉0,1≤q〈p,and p^＊=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.

Multiple Solutions for a Class of Variable-Order Fractional Laplacian Equations with Concave-Convex Nonlinearity

This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in RN, s(⋅) ∈ C (RN × RN, (0,1)), (-Δ)s(⋅) is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.

An Efficient Federated Learning Framework Deployed in Resource-Constrained IoV:User Selection and Learning Time Optimization Schemes

In this article,an efficient federated learning(FL)Framework in the Internet of Vehicles(IoV)is studied.In the considered model,vehicle users implement an FL algorithm by training their local FL models and sending their models to a base station(BS)that generates a global FL model through the model aggregation.Since each user owns data samples with diverse sizes and different quality,it is necessary for the BS to select the proper participating users to acquire a better global model.Meanwhile,considering the high computational overhead of existing selection methods based on the gradient,the lightweight user selection scheme based on the loss decay is proposed.Due to the limited wireless bandwidth,the BS needs to select an suitable subset of users to implement the FL algorithm.Moreover,the vehicle users’computing resource that can be used for FL training is usually limited in the IoV when other multiple tasks are required to be executed.The local model training and model parameter transmission of FL will have significant effects on the latency of FL.To address this issue,the joint communication and computing optimization problem is formulated whose objective is to minimize the FL delay in the resource-constrained system.To solve the complex nonconvex problem,an algorithm based on the concave-convex procedure(CCCP)is proposed,which can achieve superior performance in the small-scale and delay-insensitive FL system.Due to the fact that the convergence rate of CCCP method is too slow in a large-scale FL system,this method is not suitable for delay-sensitive applications.To solve this issue,a block coordinate descent algorithm based on the one-step projected gradient method is proposed to decrease the complexity of the solution at the cost of light performance degrading.Simulations are conducted and numerical results show the good performance of the proposed methods.

An Energy Efficient Design for UAV Communication With Mobile Edge Computing

This paper considers a UAV communication system with mobile edge computing(MEC).We minimize the energy consumption of the whole system via jointly optimizing the UAV's trajectory and task assignment as well as CPU's computational speed under the set of resource constrains.To this end,we first derive the energy consumption model of data processing,and then obtain the energy consumption model of fixed-wing UAV's flight.The optimization problem is mathematically formulated.To address the problem,we first obtain the approximate optimization problem by applying the technique of discrete linear state-space approximation,and then transform the non-convex constraints into convex by using linearization.Furthermore,a concave-convex procedure(CCCP) based algorithm is proposed in order to solve the optimization problem approximately.Numerical results show the efficacy of the proposed algorithm.

ANISOTROPIC(p,q)-EQUATIONS WITH COMPETITION PHENOMENA

We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

L_(2,1)-norm robust regularized extreme learning machine for regression using CCCP method

As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to noise and outliers.To solve this problem,L_(2,1)-norm is introduced to ELM and an L_(2,1)-norm robust regularized ELM(L_(2,1)-RRELM)was proposed.L_(2,1)-RRELM gives constant penalties to outliers to reduce their adverse effects by replacing least square loss function with a non-convex loss function.In light of the non-convex feature of L_(2,1)-RRELM,the concave-convex procedure(CCCP)is applied to solve its model.The convergence of L_(2,1)-RRELM is also given to show its robustness.In order to further verify the effectiveness of L_(2,1)-RRELM,it is compared with the three popular extreme learning algorithms based on the artificial dataset and University of California Irvine(UCI)datasets.And each algorithm in different noise environments is tested with two evaluation criterions root mean square error(RMSE)and fitness.The results of the simulation indicate that L_(2,1)-RRELM has smaller RMSE and greater fitness under different noise settings.Numerical analysis shows that L_(2,1)-RRELM has better generalization performance,stronger robustness,and higher anti-noise ability and fitness.