This paper is concerned with a third-order nonlinear separated boundary value problem. By the Leray-Schauder degree theory and the method of upper and lower solutions, we obtain the existence of at least three solutions to the problem.
Xiaojie Lin, Benshen Zhao (School of Mathematical Sciences, Xuzhou Normal University, Xuzhou 221116, Jiangsu)
In this paper,we study a class of predator-prey models with Beddington-De Angelis functional response.And the predator equation has singularity in zero prey population,where a smoothing auxiliary function is introduced to overcome it.Our aim is to see if the predator and prey can eventually survive when an alien predator enters the habitat of an existing prey by employing traveling wave solutions,based on the upper and lower solutions and Schauder’s fixed point theorem.In addition,the non-existence of traveling wave solutions is discussed by the comparison principle.At the same time,some simulations are carried out to further verify the results.
A class of combustion problem with shock layers is considered.A modified perturbation method is presented.Using this simple and valid technique,we construct the boundary and the shock layers solution to the problem,and the asymptotic behavior of the solution is discussed.The modifying perturbation method is shown to be a valid method.
