A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principl...The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.展开更多
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a...This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.展开更多
In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced.By analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an ende...In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced.By analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an endemic steady state is discussed.By using the cross-iteration method and Schauder’s fixed point theorem,we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions.By constructing a pair of upper-lower solutions,we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.It is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave speed.Finally,numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.展开更多
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
基金Project supported by the National Natural Science Foundation of China(No.10771173)
文摘The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.
基金Supported by the National Natural Science Foundation of China(No.19971032)the second author is supported by Natural Science Foundation of Canadaby a Petro Canada Young Innovator Award.
文摘This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.
基金supported by the National Natural Science Foundation of China under Grant Nos.61305076,11871316 and 11371368.
文摘In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced.By analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an endemic steady state is discussed.By using the cross-iteration method and Schauder’s fixed point theorem,we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions.By constructing a pair of upper-lower solutions,we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.It is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave speed.Finally,numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.
