Boundedness of Solutions of Quasi-periodic p-Laplacian Equations with Jumping Nonlinearity.

In this article, we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation (ϕp(x′))′ + aϕp(x+) − bϕp(x−)= g(x,t) + f(t), where g(x,t) and f(t) are quasi-periodic in t with Diophantine frequency. A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation. [ABSTRACT FROM AUTHOR]