An Inequality which Arises in the Absence of the Mountain Pass Geometry

Volume 3, Issue 3, 2002

Article 32

AN INEQUALITY WHICH ARISES IN THE ABSENCE OF THE MOUNTAIN PASS GEOMETRY

BABES-BOLYAI UNIVERSITY
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE
3400 CLUJ, ROMANIA.
E-Mail: r.precup@math.ubbcluj.ro

Received 8 February, 2001; Accepted 18 February, 2002.
Communicated by: L. Gajek

ABSTRACT. An integral inequality is deduced from the negation of the geometrical condition in the bounded mountain pass theorem of Schechter, in a situation where this theorem does not apply. Also two localization results of non-zero solutions to a superlinear boundary value problem are established.

Key words:
Integral inequality, Mountain pass theorem, Laplacean, Boundary value problem, Sobolev space.

2000 Mathematics Subject Classification:
26D10, 58E05, 35J65.

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