Abstract
The paper examines a particular class of nonlinear integro-differential equations consisting
of a Sturm-Liouville boundary value problem on the half-line, where the coefficient of
the differential term depends on the unknown function by means of a scalar integral operator.
In order to handle the nonlinearity of the problem, we consider a fixed point iteration
procedure, which is based on considering a sequence of classical Sturm-Liouville boundary
value problems in the weak solution sense. The existence of a solution and the global
convergence of the fixed-point iterations are stated without resorting to the Banach fixed
point theorem. Moreover, the unique solvability of the problem is discussed and several
examples with unique and non-unique solutions are given.
Anno
2014
Autori IAC
Tipo pubblicazione
Altri Autori
P. Junghanns, W. Themistoclakis, A. Vecchio,
Editore
Pergamon,
Rivista
Nonlinear analysis