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Oscillation criteria for half-linear elliptic inequalities with -Laplacians via Riccati method

✍ Scribed by Norio Yoshida

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 273 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.12.011

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✦ Synopsis

Riccati inequality for half-linear elliptic inequalities with p(x)-Laplacians is established, and oscillation criteria are derived by using the Riccati inequality. Our method is to reduce oscillation problems for half-linear elliptic inequalities with p(x)-Laplacians to onedimensional Riccati inequality with variable exponents. Generalizations to more general elliptic inequalities with p(x)-Laplacians are also discussed.

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The conditions on the function c x : ‫ޒ‬ ª ‫ޒ‬ are derived, which ensure that the Ž5 5 py 2 . Ž .< < py 2 PDE div ٌu ٌu q c x u u s 0, p ) 1, is oscillatory; i.e., ϱ belongs to Ä the closure of the set of zeros of every solution defined on the domain ⍀ s x g n 5 5 4 ‫ޒ‬ : x ) 1 . The main tool is th