Asymptotics of Nonlinearities and Operator Equations

A Priori Solution Estimates for Nonlinear Vector Integral Equations

“…[8] and [15]). Clearly, our Theorem 5.1 allows us to consider more general nonlinearities than ones satisfying (6.10) and (6.11).…”

Periodic solutions of systems with asymptotically evennonlinearities

“…The identity (6) [3]. The combination of (6) with the condition that f(t,x)-O has not been considered before.…”

“…In specific examples, conditions (13) and (14) are often not as awkward (see [3]) as may at first seem, e.g. in the case of Theorem 1, the relation (5) guarantees both (13) and (14).…”

On the Hopf Bifurcation in Control Systems with a Bounded Nonlinearity Asymptotically Homogeneous at Infinity

“…For solvability of problems with bounded functional nonlinearities, the asymptotic Landesman Lazer condition plays a major role ( [8,Sects 24,25]; see also [4,5,17,19]). In the context here, it suggests that the nonlinearity f (x) has finite limits as x Ä \ .…”

“…In the context here, it suggests that the nonlinearity f (x) has finite limits as x Ä \ . The superposition operator generated by such a nonlinearity has the following principal property [8],…”