We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavio...We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.展开更多
Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is imp...Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.展开更多
Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic bounda...Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.展开更多
Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
This paper is concerned with the contact process with random vertex weights on regular trees, and studies the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In th...This paper is concerned with the contact process with random vertex weights on regular trees, and studies the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection propagates through the edge connecting vertices x and y at rate λp（x）p（y） for someλ 〉0, where {ρ（x）, x∈ Td} are independent and identically distributed （i.i.d.） vertex weights. We show that when d is large enough, there is a phase transition at At（d）∈ （0, ec） such that for λ 〈 λc（d）, the contact process dies out, and for λ 〉 λc（d）, the contact process survives with a positive probability. Moreover, we also show that there is another phase transition at λe（d） such that for λ 〈 λe（d）, the contact process dies out at an exponential rate. Finally, we show that these two critical values have the same asymptotic behavior as d increases.展开更多
By using Karamata regular variation theory and upper and lower solution method,we investigate the existence and the global asymptotic behavior of large solutions to a class of semilinear elliptic equations with nonlin...By using Karamata regular variation theory and upper and lower solution method,we investigate the existence and the global asymptotic behavior of large solutions to a class of semilinear elliptic equations with nonlinear convection terms.In our study,the weight and nonlinearity are controlled by some regularly varying functions or rapid functions,which is very different from the conditions of previous contexts.Our results largely extend the previous works,and prove that the nonlinear convection terms do not affect the global asymptotic behavior of classical solutions when the index of the convection terms change in a certain range.展开更多
This paper is concerned with a diffusive West Nile virus model （WNv） in a heterogeneous environment. The basic reproduction number R0 for spatially homogeneous model is first introduced. We then define a threshold p...This paper is concerned with a diffusive West Nile virus model （WNv） in a heterogeneous environment. The basic reproduction number R0 for spatially homogeneous model is first introduced. We then define a threshold parameter R0N for the corresponding diffusive WNv model in a heterogeneous environment. It is shown that if R0^N 〉 1, the model admits at least one nontrivial T-periodic solution, whereas if RN 〈 1, the model has no nontrivial T-periodic solution. By means of monotone iterative schemes, the true solution can be obtained and the asymptotic behavior of periodic solutions is presented. The paper is closed with some numerical simulations to illustrate our theoretical results.展开更多
基金supported by the JSPS KAKENHI(JP22K03386)supported by the JST SPRING(JPMJSP2132)。
文摘We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.
文摘Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.
文摘Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.
文摘Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
文摘This paper is concerned with the contact process with random vertex weights on regular trees, and studies the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection propagates through the edge connecting vertices x and y at rate λp（x）p（y） for someλ 〉0, where {ρ（x）, x∈ Td} are independent and identically distributed （i.i.d.） vertex weights. We show that when d is large enough, there is a phase transition at At（d）∈ （0, ec） such that for λ 〈 λc（d）, the contact process dies out, and for λ 〉 λc（d）, the contact process survives with a positive probability. Moreover, we also show that there is another phase transition at λe（d） such that for λ 〈 λe（d）, the contact process dies out at an exponential rate. Finally, we show that these two critical values have the same asymptotic behavior as d increases.
基金Supported by Startup Foundation for Docotors of Weifang University(2016BS04)
文摘By using Karamata regular variation theory and upper and lower solution method,we investigate the existence and the global asymptotic behavior of large solutions to a class of semilinear elliptic equations with nonlinear convection terms.In our study,the weight and nonlinearity are controlled by some regularly varying functions or rapid functions,which is very different from the conditions of previous contexts.Our results largely extend the previous works,and prove that the nonlinear convection terms do not affect the global asymptotic behavior of classical solutions when the index of the convection terms change in a certain range.
文摘This paper is concerned with a diffusive West Nile virus model （WNv） in a heterogeneous environment. The basic reproduction number R0 for spatially homogeneous model is first introduced. We then define a threshold parameter R0N for the corresponding diffusive WNv model in a heterogeneous environment. It is shown that if R0^N 〉 1, the model admits at least one nontrivial T-periodic solution, whereas if RN 〈 1, the model has no nontrivial T-periodic solution. By means of monotone iterative schemes, the true solution can be obtained and the asymptotic behavior of periodic solutions is presented. The paper is closed with some numerical simulations to illustrate our theoretical results.
