engleski

Non-monotonic behavior of one-signed solutions of quasilinear differential equations

We consider a class of the second-order quasilinear differential equations. By deriving relations between certain types of monotonic solutions of the quasilinear equation and corresponding reciprocal half-linear equation on a finite interval $(a, b)$, we obtain criteria for all solutions of the main equation, which do not change sign in $(a, b)$, to be non-monotonic in $(a, b)$. This work is also extended to a perturbed half-linear equation as well as to the half-line $(a, \infty)$.

monotone properties ; non-monotonic behaviour ; reciprocal equation ; quasilinear ; nonlinear perturbation ; nonlinear oscillation

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