×

zbMATH — the first resource for mathematics

A second-order nonlinear difference equation: oscillation and asymptotic behavior. (English) Zbl 0508.39005

MSC:
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
Citations:
Zbl 0065.320
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atkinson, F.V., On second-order non-linear oscillations, Pacific J. math., 5, 643-647, (1955) · Zbl 0065.32001
[2] Hartman, P., Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity, Trans. amer. math. soc., 246, 1-30, (1978) · Zbl 0409.39001
[3] Hartman, P.; Wintner, A., On linear difference equations of the second order, Amer. J. math., 72, 124-128, (1950) · Zbl 0035.05803
[4] Heidel, J.W., A short proof of Atkinson’s oscillation theorem, SIAM rev., 11, 389-390, (1969) · Zbl 0169.11302
[5] Hinton, D.B.; Lewis, R.T., Spectral analysis of second order difference equations, J. math. anal. appl., 63, 421-438, (1978) · Zbl 0392.39001
[6] Patula, W.T.; Hooker, J.W., Riccati type transformations for second order linear difference equations, J. math. anal. appl., 82, 451-462, (1981) · Zbl 0471.39007
[7] Patula, W.T., Growth and oscillation properties of second order linear difference equations, SIAM J. math. anal., 10, 1, 55-61, (1979) · Zbl 0397.39001
[8] Patula, W.T., Growth, oscillation, and comparison theorems for second order linear difference equations, SIAM J. math. anal., 10, 6, 1272-1279, (1979) · Zbl 0433.39005
[9] Utz, W.R., Properties of solutions of u″ + g(t)u2n − 1 = 0, II, Monatsh. math., 69, 353-361, (1965) · Zbl 0144.10701
[10] Wong, J.S.W., On the generalized Emden-Fowler equation, SIAM rev., 17, 339-360, (1975) · Zbl 0295.34026
[11] Wouk, A., Difference equations and j-matrices, Duke math. J., 20, 141-159, (1953) · Zbl 0051.07201
[12] Szmanda, B., Oscillation theorems for nonlinear second-order difference equations, J. math. anal. appl., 79, 90-95, (1981) · Zbl 0455.39004
[13] Bykov, Ya.V.; Ševcov, E.I., Sufficient conditions for oscillation of solutions of non-linear finite difference equations, Differencial’nye uravnenija, 9, 2241-2244, (1973)
[14] Bykov, Ya.V.; Živogladova, L.V., On the oscillation of solutions of nonlinear finite difference equations, Differencial’nye uravnenija, 9, 2080-2081, (1973)
[15] Bykov, Ya.V.; Živogladova, L.V.; Ševcov, E.I., Sufficient conditions for oscillation of solutions of nonlinear finite difference equations, Differencial’nye uravnenija, 9, 1523-1524, (1973)
[16] Weil, F., Existence theorem for the difference equation yn + 1 − 2yn + yn − 1 = h2f(yn), Internat. J. math. math. sci., 3, 1, 69-77, (1980)
[17] Mingarelli, A.B., Volterra-Stieltjes integral equations and generalized differential equations, () · Zbl 0574.47004
[18] Potts, R.B., Exact solution of a difference approximation to Duffing’s equation, J. austral. math. soc. (series B), 23, 64-77, (1981) · Zbl 0475.34008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.