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MULTIPLE SOLUTIONS FOR A CLASS OF NONLINEAR EQUATIONS VIA THE MOUNTAIN PASS THEOREM


JENICĂ CRÎNGANU
"Dunărea de Jos" University of Galaţi, Department of Mathematics, Galaţi, Romania, e-mail: jcringanu@ugal.ro

Issue:

SSRSMI, Number 1, Volume XXI

Section:

Volume 21, Number 1

Abstract:

The aim of this paper is to study the existence of the multiple solutions

for the abstract equation Jp u=Nf u, where Jp is the duality mapping on a real reflexive and smooth Banach space X, corresponding to the gauge function φ(t)=tp-1, 1

It is assumed that X is compactly imbedded in Lq(Ω), where Ω is a bounded domain in RN,N≤2, 1

In order to prove the existence of the multiple solutions we use a multiple variant of the the Mountain Pass theorem.

Keywords:

p-Laplacian, Duality mapping, Mountain Pass theorem.

Code [ID]:

SSRSMI201101V21S01A0008 [0003410]

Full paper:

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