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International Journal of Differential Equations
Volume 2016, Article ID 3149482, 14 pages
Research Article

Multiplicity Results for the -Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

College of Sciences at Dammam, University of Dammam, Dammam 31441, Saudi Arabia

Received 5 April 2016; Accepted 22 June 2016

Academic Editor: Julio D. Rossi

Copyright © 2016 K. Saoudi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the singular Neumann problem involving the -Laplace operator:   , in  , where is a bounded domain with boundary, is a positive parameter, and , and are assumed to satisfy assumptions (H0)(H5) in the Introduction. Using some variational techniques, we show the existence of a number such that problem has two solutions for one solution for , and no solutions for .