Dhruba R. Adhikari
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 p-Laplacian with and time-dependent 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
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