Oscillation of Second-Order Sublinear Impulsive Differential Equations

A. Zafer

Abstract and Applied Analysis, 2011, vol. 2011, 1-11

Abstract:

Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: ð ‘¥ ′ ′ ( ð ‘¡ ) + ð ‘ ( ð ‘¡ ) | ð ‘¥ ( ð œ ( ð ‘¡ ) ) | ð ›¼ − 1 ð ‘¥ ( ð œ ( ð ‘¡ ) ) = 0 , ð ‘¡ ≠𠜃 𠑘 ; Δ ð ‘¥ ′ ( ð ‘¡ ) | ð ‘¡ = 𠜃 𠑘 + ð ‘ž 𠑘 | ð ‘¥ ( ð œ ( 𠜃 𠑘 ) ) | ð ›¼ − 1 ð ‘¥ ( ð œ ( 𠜃 𠑘 ) ) = 0 ; Δ ð ‘¥ ( ð ‘¡ ) | ð ‘¡ = 𠜃 𠑘 = 0 , ( 0 < ð ›¼ < 1 ) by considering the cases ð œ ( ð ‘¡ ) ≤ ð ‘¡ and ð œ ( ð ‘¡ ) = ð ‘¡ , respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:458275

DOI: 10.1155/2011/458275

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