Oscillation of Second-Order Sublinear Impulsive Differential Equations

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Zafer A.

ABSTRACT AND APPLIED ANALYSIS, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2011
  • Doi Number: 10.1155/2011/458275
  • Journal Name: ABSTRACT AND APPLIED ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: Yes

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: x ''(t) + p(t)vertical bar x(tau(t))vertical bar(alpha-1)x(tau(t)) = 0, t not equal theta(k); Delta x'(t)vertical bar(t=theta k) + q(k)vertical bar x(tau(theta(k)))vertical bar(alpha-1)x(tau(theta(k))) = 0; Delta x(t)vertical bar(t=theta k) = 0, (0 < alpha < 1) by considering the cases tau(t) <= t and tau(t) = t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.