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A MULTIPLICITY THEOREM FOR A VARIABLE EXPONENT DIRICHLET PROBLEM

Published online by Cambridge University Press:  01 May 2008

NIKOLAOS S. PAPAGEORGIOU  and
EUGÉNIO M. ROCHA
NIKOLAOS S. PAPAGEORGIOU
Affiliation:
Dept. of Mathematics, National Technical University, Athens, Greece e-mail: npapg@math.ntua.gr
EUGÉNIO M. ROCHA*
Affiliation:
Dept. of Mathematics, University of Aveiro, Portugal e-mail: eugenio@mat.ua.pt
*
*The corresponding author.
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Abstract

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We consider a nonlinear Dirichlet problem driven by the p(ċ)-Laplacian. Using variational methods based on the critical point theory, together with suitable truncation techniques and the use of upper-lower solutions and of critical groups, we show that the problem has at least three nontrivial solutions, two of which have constant sign (one positive, the other negative). The hypotheses on the nonlinearity incorporates in our framework of analysis, both coercive and noncoercive problems.

Keywords

35J6035J7058E05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 335 - 349
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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