Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 379, Issue 2191, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2019.0377
Keywords
accretive operator; set-valued map; topological degree; single-valued approximations; system of elliptic PDE
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Funding
- Lodz University of Technology
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In this paper, a coincidence degree construction is provided as a homotopy invariant for detecting the existence of solutions of equations. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities.
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 is an element of F(x), x is an element of U, where A:D(A) (sic) E is an m-accretive operator in a Banach space E, F:K(sic)E is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K subset of E. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.
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