Periodic solutions for \(p\)-Laplacian Rayleigh equations with a deviating argument (Q880289)

The authors investigate the existence of \(\omega\)-periodic solutions for the \(p\)-Laplacian Rayleigh equation with deviating argument of the form \[ (\phi_p(x'(t)))'+f(x'(t))+g(x(t-\tau(t)))=e(t), \] where \(f,g,e\) and \(\tau\) are real continuous functions on \(R\), \(\tau\) and \(e\) are \(\omega\)-periodic with \(\omega>0\). Some new criteria are established for the existence of \(\omega\)-periodic solutions. The method involves the generalized Borsuk theorem in the coincidence degree theory.