Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps

We apply Monch type fixed point theorems for acyclic multivalued maps to the solvability of inclusions of Hammerstein type in Banach spaces. Our approach makes possible to unify and improve the existence theories for nonlinear evolution problems and abstract integral inclusions of Volterra and Fredholm type.

Jean-François Couchouron
France

Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania

Fixed point, multivalued map, acyclic set, integral inclusion, Hammerstein equation, evolution equation, boundary value problem.

J.-F. Couchouron, R. Precup, Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps, Electron. J. Differential Equations. 2002 (2002), no.4, 1-21.

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https://ejde.math.txstate.edu/Volumes/2002/04/couchouron.pdf

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MR: 1872799, Zbl 0991.47050

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