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Displaying similar documents to “Inequalities for logarithmic and exponential functions.”

Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations

N. Parhi (2011)

Mathematica Bohemica

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In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form Δ ( p n - 1 Δ y n - 1 ) + q y n = 0 , n 1 , where q is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type Δ ( p n - 1 Δ y n - 1 ) + q n g ( y n ) = f n - 1 , n 1 , where, unlike earlier works, f n 0 or 0 (but ¬ 0 ) for large n . Further, these results are...