Positive periodic solutions of nonlinear functional differential equations
The authors investigates the existence of positive periodic solutions for the first-order functional-differential equation \[ x'(t)= -a(t) x(t)+ f(t, x_t),\tag{\(*\)} \] where \(a(t)\) is a \(T\)-periodic function satisfying \[ \exp\Biggl(\int^T_0 a(u) du\Biggr)> 1, \] \(f(t, x_t)\) is a nonnegative function defined on \(\mathbb{R}\times BC\), where \(BC\) denotes the Banach space of bounded continuous functions. By using a generalized form of the Leggett-Williams fixed-point theorem, the authors obtain some sufficient conditions for equation \((*)\) to have at least two positive \(T\)-periodic solutions.
scientific article; zbMATH DE number 2118019