Asymptotic Behavior Of Positive Solutions For A Class Of Reaction-diffusion Equations

This paper is concerned with the asymptotic profiles of positive solutions for diffusive Logistic equtions.The main paper is divided into the following two parts.Firstly,we study the influence of nonlinear terms on the asymptotic behavior of positive solutions of a class of diffusive Logistic equations.When the parameters in nonlinear terms satisfy various relations,we obtain the profiles of positive solutions.Moreover,we study the limiting profiles of the unique positive solutions of the corresponding nonlocal equations.Secondly,we investigated the effects of linear and nonlinear terms on the limit behavior of positive solutions.The asymptotic behavior of positive solutions is investigated by the upper-lower solutions method.Finally,we discuss the asymptotic behavior of the corresponding nonlocal diffusive Logistic equations.The investigation of asymptotic profiles reveals that there exist different profiles between nonlocal and local problems.