Periodic solutions of \(p\)-Laplacian equations via rotation numbers
The authors prove existence and multiplicity results for periodic solutions of the \(p\)-Laplacian equation \[ (|x'|^{p-2}x')' + f(t,x) = 0. \] Both asymptotically linear and superlinear nonlinearities are studied, in absence of global existence and uniqueness conditions on the solutions of the associated Cauchy problems. Some classical results for second order differential equations (i.e., the case \(p=2\)) are thus extended. The proofs make use of a recent version of the Poincaré-Birkhoff theorem provided by Fonda and Ureña.
rotation number, Poincaré-Birkhoff theorem
scientific article; zbMATH DE number 7359982
scientific article