A MULTIPLICITY THEOREM FOR A VARIABLE EXPONENT DIRICHLET PROBLEM
Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 335-349
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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.
PAPAGEORGIOU, NIKOLAOS S.; ROCHA, EUGÉNIO M. A MULTIPLICITY THEOREM FOR A VARIABLE EXPONENT DIRICHLET PROBLEM. Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 335-349. doi: 10.1017/S0017089508004242
@article{10_1017_S0017089508004242,
author = {PAPAGEORGIOU, NIKOLAOS S. and ROCHA, EUG\'ENIO M.},
title = {A {MULTIPLICITY} {THEOREM} {FOR} {A} {VARIABLE} {EXPONENT} {DIRICHLET} {PROBLEM}},
journal = {Glasgow mathematical journal},
pages = {335--349},
year = {2008},
volume = {50},
number = {2},
doi = {10.1017/S0017089508004242},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004242/}
}
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