Abstract
We investigate second-order half-linear differential equations with asymptotically almost periodic coefficients. For these equations, we explicitly find an oscillation constant. If the coefficients are replaced by constants, our main result (concerning the conditional oscillation) reduces to the classical one. We also mention examples and concluding remarks. MSC:34C10, 34C15.
Highlights
1 Introduction This paper is devoted to the study of the half-linear differential equation r(t) x + c(t) (x) =, (x) = |x|p– sgn x, ( . )
The name half-linear equations was introduced in [ ]. This term is motivated by the fact that the solution space of these equations is homogeneous, but it is not additive
Some tools widely used in the theory of linear equations are not available for half-linear equations
Summary
This paper is devoted to the study of the half-linear differential equation r(t) x + c(t) (x) = , (x) = |x|p– sgn x, The name half-linear equations was introduced in [ ] This term is motivated by the fact that the solution space of these equations is homogeneous (likewise in the linear case), but it is not additive. Some tools widely used in the theory of linear equations are not available for half-linear equations (e.g., see [ ] for the Wronskian identity and [ ] for the Fredholm alternative). These differences are caused, more or less, by the lack of the additivity.
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