International Journal of Pure and Applied Mathematics Volume 96 No. 1 2014, 117-134 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v96i1.9 P A ijpam.eu GLOBAL PROPERTIES OF SOLUTIONS OF FOURTH ORDER GENERALIZED α-DIFFERENCE EQUATIONS M. Maria Susai Manuel 1 § , K. Srinivasan 2 , D.S. Dilip 3 , G. Dominic Babu 4 1 Department of Science and Humanities R.M.D. Engineering College Kavaraipettai, 601 206, Tamil Nadu, S. INDIA 2 Department of Science and Humanities S.K.P. Institute of Technology Tiruvannamalai, Tamil Nadu, S. INDIA 3 Department of Mathematics St. John’s College Anchal, Kollam District, Kerala, INDIA 4 Department of Mathematics Sacred Heart College Tirupattur, 635 601, Vellore District Tamil Nadu, S. INDIA Abstract: In this paper, the authors discuss various properties of solutions for the generalized α−difference equation Δ 4 α(ℓ) u(k − 2ℓ)= α 2 p(k)u(k), k ∈ [2ℓ, ∞), (1) where the functions p is positive on [2ℓ, ∞), α> 1 and ℓ is a positive real. AMS Subject Classification: 39A, 12 Key Words: generalized α−difference equation, generalized α−difference operator, oscillation and nonoscillation Received: July 9, 2014 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author