Abstract. We investigate some sufficient conditions for the solutions of the equations below, extended to the whole space to be oscillatory, using only some Picone-type formulas. Some uniqueness results are given. The important fact of the use of the Picone-type formulas displayed here is that it leads to some interesting results with some easy hypotheses. In Part II we extend the results to some known equations, using some comparison results.

Received: March 2, 2011

AMS Subject Classification: 35J60, 35J70

Key Words and Phrases: Picone's identity, quasilinear elliptic equations

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