Solutions of implicit evolution inclusions with pseudo-monotone mappings

Wenming Bian

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.

Keywords


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

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