SOME MULTIPLICITY RESULTS TO THE EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET BOUNDARY VALUE PROBLEM INVOLVING THE P-LAPLACIAN | Zendy

Shapour Heidarkhani | Zendy; G. A. Afrouzi | Zendy

Open Access

SOME 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

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].

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