Existence of periodic solutions for \(p\)-Laplacian equation without growth restrictions
The paper investigates the periodic \(p\)-Laplacian differential equation \[ (|x'|^{p-2}x')'=f(t,x,x'), \] where \(p>1\) and \(f\) is a continuous function, \(T\)-periodic in the \(t\)-variable. The use of a topological transversality method and a barrier strip technique allows the authors to obtain the existence of \(T\)-periodic solutions without growth assumptions on \(f\) (at \(0\) and at infinity). Moreover, an application to a Rayleigh-type \(p\)-Laplacian equation is illustrated.
scientific article; zbMATH DE number 7349809
scientific article