Session 7. Difference equations and their application in the mathematical modeling

Oscillatory properties for second order nonlinear difference equations of neutral type

Agata Bezubik, Insitute of Mathematics, University of Białystok, Poland
In this talk we consider the nonlinear difference equations \[\Delta(a_n\Delta(x_n-p_nx_{n-1}))+f(n,x_{n-\delta})=0.\] We present some criteria of the oscillation of solutions of the above equations.
References
  1. R.P. Agarwal, M. Bohner, S.R. Grace and D. O'Regan, Discrete Oscillation Theory , Hindawi Publishing Corporation, New York, 2005.
  2. M. Migda, A. Musielak, E. Schmeidel, Oscillatory of fourth order nonlinear difference equations with quasidifferences , Opuscula Math., Vol. 26(2), 371--380, (2006).
  3. M. Migda Oscillation and nonoscillation results for higher-order nonlinear difference equations , Fields Institute Communications, Vol. 42, 285--294, (2004).
  4. E. Schmeidel, Z. Zbąszyniak, An Application of Darbo's Fixed Point Theorem in Investigation of Periodicity of Solutions of Difference Equations, Comput. Math. Appl., Vol. 64 (7), 2185–--2191, (2012).
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