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arXiv · 2008.06579

Degree for weakly upper semicontinuous perturbations of quasi-$m$-accretive operators

Wojciech Kryszewski·Mateusz Maciejewski
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Abstract

In the paper we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in a Banach space $ E$, $F\colon K\multimap E$ is a weakly upper semicontinuous set-valued map constrained to an open subset $U$ of a closed set $K\subset E$. Two different approaches will be presented. The theory is applied to show the existence of nontrivial positive solutions of some nonlinear second order partial differential equations with discontinuities.

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Wojciech Kryszewski, Mateusz Maciejewski. 2020-08-14. Degree for weakly upper semicontinuous perturbations of quasi-$m$-accretive operators. https://doi.org/10.1098/rsta.2019.0377

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