In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the seri...In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.展开更多
In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
In this paper,a SVEIRDP epidemic model is proposed to investigate the transmission dynamics of Ebola by cumulative release from the infected individuals and corpses in the form of infinite integrals.First,the positivi...In this paper,a SVEIRDP epidemic model is proposed to investigate the transmission dynamics of Ebola by cumulative release from the infected individuals and corpses in the form of infinite integrals.First,the positivity and ultimate boundedness of solutions are proved.Second,the basic reproduction number R0 is calculated.Furthermore,it is proven that if R0<1,the model has the disease-free equilibrium and is globally asymptotically stable(GAS);If R0>1,the unique endemic equilibrium is GAS.To clearly illustrate the theoretical results,real data are used to conduct numerical simulations.We discover that modeling the cumulative release of Ebola from the infected individuals and corpses using the infinite integral with an appropriate probability density function(PDF)provides a more realistic and accurate representation of the actual disease spread.展开更多
文摘In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
基金supported by the Natural Science Foundation of China(Grant No.12261087,12371504,12201540)the Natural Science Foundation of Xinjiang,China(Grant No.2022D01E41)+1 种基金the Leading Talents of Tianshan Project in Xinjiang Uygur Autonomous Region,China(Grant No.2023TSYCLJ0054)the Open Project of Key Laboratory of Applied Mathematics of Xinjiang,China(Grant No.2021D04014).
文摘In this paper,a SVEIRDP epidemic model is proposed to investigate the transmission dynamics of Ebola by cumulative release from the infected individuals and corpses in the form of infinite integrals.First,the positivity and ultimate boundedness of solutions are proved.Second,the basic reproduction number R0 is calculated.Furthermore,it is proven that if R0<1,the model has the disease-free equilibrium and is globally asymptotically stable(GAS);If R0>1,the unique endemic equilibrium is GAS.To clearly illustrate the theoretical results,real data are used to conduct numerical simulations.We discover that modeling the cumulative release of Ebola from the infected individuals and corpses using the infinite integral with an appropriate probability density function(PDF)provides a more realistic and accurate representation of the actual disease spread.
