Precise asymptotic behavior of solutions to damped simple pendulum equations.
Abstract. Applying the topological transversality method of Granas and the a priori bounds technique, we prove some existence theorems for diflerential inclusions of the form x" ∈ F(t, x, x'), x ∈ ℬ, where F is a Carathéodory multifunction with convex, compact values. No growth condition will be imposed on F.
The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.