IJPAM: Volume 106, No. 1 (2016)

ON A NEW FIXED POINT THEOREM ON HILBERT
SPACES VIA THE MOUNTAIN PASS LEMMA AND
APPLICATIONS TO ELLIPTIC BOUNDARY
VALUE PROBLEMS

Ayadi Souad$^1$, Toufik Moussaoui$^2$, Donal O'Regan$^3$
$^1$Laboratory of Physical Mechanics and Mathematical Modeling
Medea, ALGERIA
$^1$Laboratory of Fixed Point Theory and Applications
Department of Mathematics
E.N.S. Kouba, Algiers, ALGERIA
$^2$Laboratory of Fixed Point Theory and Applications
Department of Mathematics
E.N.S. Kouba, Algiers, ALGERIA
$^3$School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Galway, IRELAND


Abstract. In this paper we present a new fixed point theorem in Hilbert spaces. Using a suitable critical point theorem we provide conditions under which potential operators have a fixed point. An application is given to illustrate the theory.

Received: January 18, 2016

AMS Subject Classification:

Key Words and Phrases: fixed point theorem, potential operators

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DOI: 10.12732/ijpam.v106i1.16 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 213 - 221


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