Oscillation constants for second-order ordinary differential equations related to elliptic equations with p-Laplacian

Abstract In this paper we consider the second-order nonlinear differential equation ( ∗ ) ( t α − 1 Φ ( x ′ ) ) ′ + t α − 1 − p f ( x ) = 0 , Φ ( x ) = | x | p − 2 x , p > 1 , α ∈ R , with f satisfying x f ( x ) > 0 , x ≠ 0 . We analyze the difference between the cases α p , α > p , and α = p . In each case we give a condition on the function f which guarantees that solutions of Eq. ( ∗ ) are (non)oscillatory. The principal methods used in this paper are the Riccati technique and its modifications. The results of our paper complement and extend several previously obtained results on the subject.

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