In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, ...In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.展开更多
In this paper, the two-species prey-predator Lotka-Volterra model with the Holling＇s type III is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of ...In this paper, the two-species prey-predator Lotka-Volterra model with the Holling＇s type III is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.展开更多
It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterat...It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.展开更多
This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a ne...This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.展开更多
基金Partially supported by "one hundred distinguished young researcher fund program" of Sun Yat-Sen University
文摘In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.
基金Supported by the National Natural Science Foundation of China(1057601310871075)
文摘In this paper, the two-species prey-predator Lotka-Volterra model with the Holling＇s type III is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.
基金supported by the National Basic Research Program of China (Grant No. 2011CB302402)National Natural Science Foundation of China (Grant Nos. 61021004 and 10825104)Shanghai Leading Academic Discipline Project (Grant No. B412)
文摘It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.
基金This work was supported by the National Natural Science Foundation of China （No. 11071254）.
文摘This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.
