### Solutions of implicit evolution inclusions with pseudo-monotone mappings

DOI: http://dx.doi.org/10.12775/TMNA.2000.008

#### Abstract

Existence results are given for the implicit evolution inclusions

$(Bx(t))'+A(t, x(t))\ni f(t)$ and $(Bx(t))'+A(t, x(t))-G(t, x(t))\ni f(t)$

with $B$ a bounded linear operator, $A(t,\cdot)$ a bounded, coercive

and pseudo-monotone set-valued mapping and $G$ a set-valued mapping of

non-monotone type. Continuity of the solution set of first inclusion with

respect to $f$ is also obtained which is used to solve the second

inclusion.

$(Bx(t))'+A(t, x(t))\ni f(t)$ and $(Bx(t))'+A(t, x(t))-G(t, x(t))\ni f(t)$

with $B$ a bounded linear operator, $A(t,\cdot)$ a bounded, coercive

and pseudo-monotone set-valued mapping and $G$ a set-valued mapping of

non-monotone type. Continuity of the solution set of first inclusion with

respect to $f$ is also obtained which is used to solve the second

inclusion.

#### Keywords

Implicit differential inclusions; pseudo-monotone mappings; solution set; perturbations

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.