TY - JOUR
A2 - Migorski, Stanislaw
AU - Asfaw, Teffera M.
PY - 2017
DA - 2017/09/12
TI - A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem
SP - 7236103
VL - 2017
AB - Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T:X⊇D(T)→2X⁎ be maximal monotone, S:X→2X⁎ be bounded and of type (S+), and C:D(C)→X⁎ be compact with D(T)⊆D(C) such that C lies in Γστ (i.e., there exist σ≥0 and τ≥0 such that Cx≤τx+σ for all x∈D(C)). A new topological degree theory is developed for operators of the type T+S+C. The theory is essential because no degree theory and/or existence result is available to address solvability of operator inclusions involving operators of the type T+S+C, where C is not defined everywhere. Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. The theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces.
SN - 1085-3375
UR - https://doi.org/10.1155/2017/7236103
DO - 10.1155/2017/7236103
JF - Abstract and Applied Analysis
PB - Hindawi
KW -
ER -