Existence and nonexistence of multiple positive periodic solutions of first order differential equations with unbounded Green's kernel (Q2850045)

The authors investigate the existence of positive solutions of parametrized functional differential equations of the form NEWLINE\[NEWLINE x'(t)= a(t) g(x(t)) x(t) - \lambda b(t) f(x(h(t))). \tag{1} NEWLINE\]NEWLINE Here, \(\lambda >0\) and \(a, b, h\) are \(T\)-periodic functions. In particular they focus on the case in which the corresponding integral equations have an unbounded Green's kernel. By using the Leggett-Williams multiple fixed point theorem, they obtain results on the existence of at least two positive \(T\)-periodic solutions of (1), as well as nonexistence results, in terms of the parameter \(\lambda\).