Electron. J. Diff. Eqns., Vol. 2002(2002), No. 04, pp. 1-21.

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

Jean-Francois Couchouron & Radu Precup

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.

Submitted June 18, 2001. Published January 3, 2002.
Math Subject Classifications: 47H10, 45N05, 47J35.
Key Words: Fixed point, multivalued map, acyclic set, integral inclusion, Hammerstein equation, evolution equation, boundary value problem.

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Jean-Francois Couchouron
Universite de Metz
Mathematiques INRIA Lorraine,
Ile du Saulcy, 57045 Metz, France
e-mail: couchour@loria.fr
Radu Precup
University Babes-Bolyai,
Faculty of Mathematics and Computer Science,
3400 Cluj, Romania
e-mail: r.precup@math.ubbcluj.ro

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