In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isom...In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isometry.Moreover,by the result in Li et al.(2017),g is the Graham-Lee metric(see Graham and Lee(1991))on the unit ball B_(1)■R^(4k+4).We also give an a priori estimate of the Einstein metric g.As a byproduct of the a priori estimates,based on the estimate and Graham-Lee and Lee's seminal perturbation results(see Graham and Lee(1991)and Lee(2006)),we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity(S^(4k+3),[g])when the metric?is Sp(k+1)-invariant.We also generalize the results to the case of conformal infinity(S^(15),[?])with g a Spin(9)-invariant metric in the appendix.展开更多
We study the uniqueness and existence of solutions of reflected G-stochastic differential equations （RGSDEs） with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover, we obtain the c...We study the uniqueness and existence of solutions of reflected G-stochastic differential equations （RGSDEs） with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover, we obtain the comparison theorem for RGSDEs with nonlinear resistance.展开更多
Use of nonlinear mathematical models has been majorly based on in vitro gas production(GP) data generated when substrates are incubated with rumen liquor from fistulated steers. However,existing evidence suggests that...Use of nonlinear mathematical models has been majorly based on in vitro gas production(GP) data generated when substrates are incubated with rumen liquor from fistulated steers. However,existing evidence suggests that rumen liquor from slaughtered cattle of unknown dietary history also generates quantifiable in vitro GP data. Fitting and description of GP data obtained from 4 diets incubated with rumen liquor from slaughtered cattle was evaluated using single-pool exponential model with discrete lag time(EXPL), logistic(LOG), Groot's(GRTS) and Gompertz(GOMP) models. Diets were formulated by varying proportions of Rhodes grass(Chloris gayana) hay and a concentrate mixed on dry matter basis to be: 1,000 g/kg Rhodes grass hay(RGH) and 0 of the concentrate(D1), 900 g/kg RGH and 100 g/kg concentrate(D2), 800 g/kg RGH and 200 g/kg concentrate(D3), 700 g/kg RGH and 300 g/kg concentrate(D4). Dietary kinetics for the models were determined by measuring GP at 2,4.8,10.18,24.36,48.72,96 and 120 h. Model comparison was based on derived GP kinetics, graphical analysis of observed versus predicted GP profiles plus residual distribution and goodness-of-fit from analysis of root mean square error(RMSE), adjusted coefficient of determination(Adj-R^2) and Akaike's information criterion(AIC). Asymptotic GP, half-life and fractional rate of GP differed(P < 0.001) among the 4 models. The RMSE, Adj-R^2 and AIC ranged from 1.555 to 4.429,0.906 to0.984 and 2.452 to 15.874, respectively, forall diets compared across the 4 models. Based on the goodness-of-fit statistical criterion, GP profiles of D1 were more appropriately fitted and described by GRTS and GOMP than the EXPLand LOG models. The GRTS model had the lowest AIC value for D2(2.452). Although GRTS model had the most homogenous residual dispersion for the 4 diets, all the 4 models exhibited a sigmoidal behavior.Therefore, rumen liquor from slaughtered cattle of unknown dietary history can be used to derive nutritionally important feed parameters, but choice of the most appropriate展开更多
In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditi...In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.展开更多
A kind of infinite demensional nonlinear dynamical system described by functional differential equations with finite time delay is investigated in this paper The comparison principles of LRC type are established and a...A kind of infinite demensional nonlinear dynamical system described by functional differential equations with finite time delay is investigated in this paper The comparison principles of LRC type are established and applied to the problems of averaging principle and practical stability in terms of two measures for the system with time delay展开更多
In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are stud...In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are studied.展开更多
New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ra...New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ratios of positive odd integers, 0 〈 μ 〈 1 and λ 〉 1 are established.展开更多
This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lo...This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lower solutions and comparison principle.A threshold is defined by the eigenvalue problem of the linearized system.We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold.When the speed parameter equals to the threshold,if there exists an upper solution satisfying proper limit behavior,then the linear selection is realized.For a special function of infection rate,we obtain a threshold parameter that determines the linear and nonlinear selections.展开更多
We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all sma...We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11701326)the Fundamental Research Funds of Shandong University(Grant No.2016HW008)the Young Scholars Program of Shandong University(Grant No.2018WLJH85)。
文摘In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isometry.Moreover,by the result in Li et al.(2017),g is the Graham-Lee metric(see Graham and Lee(1991))on the unit ball B_(1)■R^(4k+4).We also give an a priori estimate of the Einstein metric g.As a byproduct of the a priori estimates,based on the estimate and Graham-Lee and Lee's seminal perturbation results(see Graham and Lee(1991)and Lee(2006)),we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity(S^(4k+3),[g])when the metric?is Sp(k+1)-invariant.We also generalize the results to the case of conformal infinity(S^(15),[?])with g a Spin(9)-invariant metric in the appendix.
基金The author would like to thank the referees for their careful reading and helpful suggestions. This work was partially supported by the China Scholarship Council （No. 201306220101）, the National Natural Science Foundation of China （Grant No. 11221061）, and the Programme of Introducing Talents of Discipline to Universities of China （No. B12023）.
文摘We study the uniqueness and existence of solutions of reflected G-stochastic differential equations （RGSDEs） with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover, we obtain the comparison theorem for RGSDEs with nonlinear resistance.
基金the Livestock and Fisheries Programme(LFP 04) of the Association for Strengthening Agricultural Research in Eastern and Central Africa(ASARECA-RC12_LFP-04 under the auspices of the World Bank for providing financial support to undertake this research
文摘Use of nonlinear mathematical models has been majorly based on in vitro gas production(GP) data generated when substrates are incubated with rumen liquor from fistulated steers. However,existing evidence suggests that rumen liquor from slaughtered cattle of unknown dietary history also generates quantifiable in vitro GP data. Fitting and description of GP data obtained from 4 diets incubated with rumen liquor from slaughtered cattle was evaluated using single-pool exponential model with discrete lag time(EXPL), logistic(LOG), Groot's(GRTS) and Gompertz(GOMP) models. Diets were formulated by varying proportions of Rhodes grass(Chloris gayana) hay and a concentrate mixed on dry matter basis to be: 1,000 g/kg Rhodes grass hay(RGH) and 0 of the concentrate(D1), 900 g/kg RGH and 100 g/kg concentrate(D2), 800 g/kg RGH and 200 g/kg concentrate(D3), 700 g/kg RGH and 300 g/kg concentrate(D4). Dietary kinetics for the models were determined by measuring GP at 2,4.8,10.18,24.36,48.72,96 and 120 h. Model comparison was based on derived GP kinetics, graphical analysis of observed versus predicted GP profiles plus residual distribution and goodness-of-fit from analysis of root mean square error(RMSE), adjusted coefficient of determination(Adj-R^2) and Akaike's information criterion(AIC). Asymptotic GP, half-life and fractional rate of GP differed(P < 0.001) among the 4 models. The RMSE, Adj-R^2 and AIC ranged from 1.555 to 4.429,0.906 to0.984 and 2.452 to 15.874, respectively, forall diets compared across the 4 models. Based on the goodness-of-fit statistical criterion, GP profiles of D1 were more appropriately fitted and described by GRTS and GOMP than the EXPLand LOG models. The GRTS model had the lowest AIC value for D2(2.452). Although GRTS model had the most homogenous residual dispersion for the 4 diets, all the 4 models exhibited a sigmoidal behavior.Therefore, rumen liquor from slaughtered cattle of unknown dietary history can be used to derive nutritionally important feed parameters, but choice of the most appropriate
基金Project Supported by the National 973 Project(G1999075100)of Chinathe ExcellentPersonnel Supporting Plan of the Ministry of Education of China.
文摘In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.
基金Project supported by the National Natural Science Foundation of ChinaSpectal Research Foundation for Ph.D. Program of State Education Commission of China
文摘A kind of infinite demensional nonlinear dynamical system described by functional differential equations with finite time delay is investigated in this paper The comparison principles of LRC type are established and applied to the problems of averaging principle and practical stability in terms of two measures for the system with time delay
基金Supported by the NNSF of China(40676016,10471039)the National Key Project for Basics Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004).
文摘In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are studied.
文摘New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ratios of positive odd integers, 0 〈 μ 〈 1 and λ 〉 1 are established.
基金supported by NSF of China (No.11971213)Natural Science Foundation of Gansu Province of China (No.21JR7RA535).
文摘This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lower solutions and comparison principle.A threshold is defined by the eigenvalue problem of the linearized system.We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold.When the speed parameter equals to the threshold,if there exists an upper solution satisfying proper limit behavior,then the linear selection is realized.For a special function of infection rate,we obtain a threshold parameter that determines the linear and nonlinear selections.
基金NNSF of China(Grant No.12071413)NSF of Guangxi(Grant No.2023GXNSFAA026085)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.
