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Some multiplicity results to the existence of three solutions for a dirichlet boundary value problem involving the p-laplacian

Abstract

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].

Keyword : three solutions, critical point, variational methods, multiplicity results, Dirichlet problem

How to Cite
Heidarkhani, S., & Afrouzi, G. (2011). Some multiplicity results to the existence of three solutions for a dirichlet boundary value problem involving the p-laplacian. Mathematical Modelling and Analysis, 16(3), 390-400. https://doi.org/10.3846/13926292.2011.601770
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Aug 24, 2011
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