Existence of maximal and minimal periodic solutions for first-order functional differential equations

Authors：Kang Shugui^*; Shi Bao; Wang Genqiang

Source：Applied Mathematics Letters, 2010, 23(1): 22-25.

DOI：10.1016/j.aml.2009.08.004

• First-order functional differential equations
• Lower and upper solutions
• Maximal and minimal periodic solutions
• Existence
• Fixed point

One important question in population models is whether periodic solutions exist and whether they are bounded between minimal and maximal solutions. This paper deals with the existence of maximal and minimal periodic solutions for the periodic solutions of a first-order functional differential equation
y'(t) = -a(t)y(t) + f(t,y(t - tau(t)))
by using the method of lower and upper solutions.

• Institution
  山西大同大学; 广东技术师范学院