Positive entire solutions for singular -Laplacian equations on with

✍ Scribed by Wu Jiong Qi

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 300 KB
• Volume: 73
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.04.073

✦ Synopsis

Suppose that constants p ≥ N ≥ 2, β ≥ 0 and that f :

This paper discusses the existence of the positive entire solutions of the singular p-Laplacian equation div(|∇u| p-2

and gives some sufficient conditions for the equation to have infinitely many positive entire solutions u(x) satisfying

where C 1 , C 1 > 0 are constants depending only on u, α(|x|) = max{1, log |x|} for p = N and α(|x|) = |x| (p-N)/(p-1) for p > N. The super-subsolution method is used to prove the existence of such solutions.