DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
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MULTIPLE POSITIVE SOLUTIONS OF SINGULAR<br />
p-LAPLACIAN PROBLEMS VIA VARIATIONAL METHODS<br />
KANISHKA PERERA AND ELVES A. B. SILVA<br />
We obtain multiple positive solutions of singular p-Laplacian problems using variational<br />
methods.<br />
Copyright © 2006 K. Perera and E. A. B. Silva. This is an open access article distributed<br />
under the Creative Commons Attribution License, which permits unrestricted use, distribution,<br />
and reproduction in any medium, provided the original work is properly cited.<br />
1. Introduction<br />
Consider the boundary value problem<br />
−Δ p u = f (x,u) inΩ,<br />
u>0 inΩ,<br />
u = 0 on∂Ω,<br />
(1.1)<br />
where Ω is a bounded domain in R n , n ≥ 1ofclassC 1,α for some α ∈ (0,1), Δ p u =<br />
div(|∇u| p−2 ∇u) isthep-Laplacian of u, 1