Open AccessSOME MULTIPLICITY RESULTS TO THE EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET BOUNDARY VALUE PROBLEM INVOLVING THE P-LAPLACIAN
Author(s) -
Shapour Heidarkhani,
G. A. Afrouzi
Publication year - 2011
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2011.601770
Subject(s) - mathematics , multiplicity (mathematics) , bounded function , p laplacian , boundary value problem , dirichlet distribution , dirichlet problem , mathematical analysis , pure mathematics , nonlinear system , dirichlet boundary condition , physics , quantum mechanics
In this paper we prove the existence of two intervals of positive real parameters λ for a Dirichlet boundary value problem involving the p-Laplacian which admit three weak solutions, whose norms are uniformly bounded with respect to λ belonging to one of the two intervals. Our main tool is a three critical points theorem due to G. Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim., 28:249–258, 2004].