AIMS Mathematics最新文献

In this paper we are concerned with the Lane-Emden-Fowler equation

begin{document}$ begin{equation*} left{begin{array}{rll}-Delta u & = u^{frac{n+2}{n-2}- varepsilon}& {rm{in}}; Omega, u&>0& {rm{in}}; Omega, u& = 0& {rm{on}}; partial Omega, end{array} right. end{equation*} $end{document}

where $ Omega subset mathbb{R}^n $ ($ n geq 3 $) is a nonconvex polygonal domain and $ varepsilon > 0 $. We study the asymptotic behavior of minimal energy solutions as $ varepsilon > 0 $ goes to zero. A main part is to show that the solution is uniformly bounded near the boundary with respect to $ varepsilon > 0 $. The moving plane method is difficult to apply for the nonconvex polygonal domain. To get around this difficulty, we derive a contradiction after assuming that the solution blows up near the boundary by using the Pohozaev identity and the Green's function.

In this paper, we investigate a min matrix and obtain its $ LU $-decomposition, determinant, permanent, inverse, and norm properties. In addition, we obtain a recurrence relation provided by the characteristic polynomial of this matrix. Finally, we present an example to illustrate the results obtained.

This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic solutions for the ordinary differential equation model, and derived the first derivative formula of periodic functions for the perturbed model. Second, applying the Floquet theory, we gave the conditions of Turing patterns occurring at Hopf bifurcating periodic solutions. Additionally, we determined the range of cross-diffusion coefficients for the diffusive population model to form Turing patterns at the stable periodic solutions. Finally, our research was summarized and the relevant conclusions were simulated numerically.

Let $ H $ be a graph with edge set $ E_H $. The Sombor index and the reduced Sombor index of a graph $ H $ are defined as $ SO(H) = sumlimits_{uvin E_H}sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $ and $ SO_{red}(H) = sumlimits_{uvin E_H}sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $, respectively. Where $ d_{H}(u) $ and $ d_{H}(v) $ are the degrees of the vertices $ u $ and $ v $ in $ H $, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $ mathcal{C}(n, k) $ be the class of cacti of order $ n $ with $ k $ cycles. In this paper, the lower bound for the Sombor index of the cacti in $ mathcal{C}(n, k) $ is obtained and the corresponding extremal cacti are characterized when $ ngeq 4k-2 $ and $ kgeq 2 $. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach.

In this article, the global well-posedness of weak solutions for 2D non-autonomous g-Navier-Stokes equations on some bounded domains were investigated by the Faedo-Galerkin method. Then the existence of pullback attractors for 2D g-Navier-Stokes equations with nonlinear damping and time delay was obtained using the method of pullback condition (PC).

Correctly determining a company's market worth during an entire year or a certain period presents a difficulty to decision-makers. In the case of the merger of companies, the need performs heavier when both the companies' owners are attracted to establishing a fair price at the optimal time to merge. The effectiveness of representing, connecting and manipulating both uncertainty and periodicity information becomes highly required. Hence, study and nhance some properties and conditions of the algebraic structure of complex hesitant fuzzy graphs. Therefore, the degree of composition between two complex hesitant fuzzy graphs is proposed. Also, the formal definitions of union, joint and complement are presented to be covered in the realm of complex hesitant fuzzy graphs. A real-life application is illustrated to show the relation between vertices and edges in the form of complex hesitant fuzzy graphs.

We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ alpha $-confidence level, $ alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ alpha $-REP.

Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.

Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results.

This paper is concerned with mathematical modeling for the development of Shandong traffic. The system dynamics model of the development of traffic in Shandong is established. In terms of this model, it is shown that highway operation as well as rail transit promotes the development of traffic, while traffic accidents inhibit traffic development. Moreover, the maximum error between the output data and the statistics bureau, based on which some forecasts for the development of traffic in the future are given, is obtained, some suggestions and optimization schemes for traffic development are given. Finally, a neural network model of the development of Shandong traffic is also derived.