Electron. J. Differential Equations,
Vol. 2017 (2017), No. 151, pp. 121.
Nontrivial solutions of inclusions involving perturbed maximal monotone
operators
Dhruba R. Adhikari
Abstract:
Let X be a real reflexive Banach space and
its dual space.
Let
be a densely defined linear maximal
monotone operator, and
,
and
,
be strongly quasibounded maximal monotone and positively
homogeneous of degree 1. Also, let
be bounded,
demicontinuous and of type
w.r.t. to D(L).
The existence of nonzero solutions of
is established
in the set
,
where
with
,
are open sets in X,
,
and
is bounded. In the special case when L=0, a mapping
of class (P) introduced by Hu and Papageorgiou
is also incorporated and the existence of nonzero solutions of
,
where T is only maximal monotone and positively
homogeneous of degree
,
is obtained. Applications to
elliptic partial differential equations involving pLaplacian with
and timedependent parabolic partial differential equations
on cylindrical domains are presented.
Submitted June 11, 2016. Published June 25, 2017.
Math Subject Classifications: 47H14, 47H05, 47H11.
Key Words: Strong quasiboundedness; Browder and Skrypnik degree theories;
maximal monotone operator; bounded demicontinuous operator
of type
.
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Dhruba R. Adhikari
Department of Mathematics
Kennesaw State University
Georgia 30060, USA
email: dadhikar@kennesaw.edu

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