Positive solutions of nonlinear problems at resonance
This article deals with the semilinear problem of the form \[ Lu= Nu, \] where \(L: D(L)\subset \mathbb{E}\to \mathbb{F}\) is a noninvertible linear operator, \(N: \mathbb{E}\to \mathbb{F}\) is a nonlinear operator, \(\mathbb{E}\) and \(\mathbb{F}\) are Banach spaces. An existence theorem in a cone which improved some earlier results of the author and the existence of a positive periodic solution of the equation \[ u''+ u+ \mu u^ 2= \varepsilon\cos \omega t \] using the method of upper and lower solution are proved.
existence of a positive periodic solution
scientific article; zbMATH DE number 148679
scientific article