6533b826fe1ef96bd1283c5c

RESEARCH PRODUCT

Global Non-monotonicity of Solutions to Nonlinear Second-Order Differential Equations

Yuriy V. RogovchenkoMervan Pašić

subject

Differential equationGeneral Mathematics010102 general mathematicsMonotonic functionInterval (mathematics)01 natural sciencesNonlinear differential equationsTerm (time)010101 applied mathematicsSecond order differential equationsNonlinear systemApplied mathematics0101 mathematicsNonlinear differential equations ; non-monotone behaviour ; second order ; damping term ; reciprocal equationSign (mathematics)Mathematics

description

We study behavior of solutions to two classes of nonlinear second-order differential equations with a damping term. Sufficient conditions for the first derivative of a solution x(t) to change sign at least once in a given interval (in a given infinite sequence of intervals) are provided. These conditions imply global non-monotone behavior of solutions.

yearjournalcountryeditionlanguage
2018-02-05Mediterranean Journal of Mathematics
https://doi.org/10.1007/s00009-018-1075-2