Some results for nonlinear equations and systems of ode's

with p-laplacian like operators.

with p-laplacian like operators.

Raul Manásevich

Centro de Modelamiento Matemático and
Departamento de Ingeniería Matemática, F.C.F.M.,
Universidad de Chile,

Casilla 170, Correo 3, Santiago, Chile

*E-mail:* manasevi@dim.uchile.cl

Let us consider the so-called one-dimensional *p*-Laplacian operator
where *p* > 1 and
is given by
for
and
Problems with separated two-point boundary value or periodic conditions
containing this operator have received a lot of attention lately with
respect
to existence and multiplicity of solutions.

Our aim in this talk is to deal with existence of periodic solutions to
some *system* cases involving fairly general vector-valued operator
Thus we will consider the boundary value problem

where the function satisfies some monotonicity conditions which ensure that is an homeomorphism onto As a consequence our results will apply to a large class of nonlinear operators which for example contain some vector versions of