Abstract
In this paper, we study the oscillatory properties of the solutions of a class of fourth-order p -Laplacian differential equations with middle term. The new oscillation criteria obtained by using the theory of comparison with first- and second-order differential equations and a refinement of the Riccati transformations. The results in this paper improve and generalize the corresponding results in the literatures. Three examples are provided to illustrate our results.
Highlights
We are concerned with the oscillation behavior of solutions of the fourth-order p-Laplacian differential equations with middle term rðtÞz
The p-Laplacian differential equations there are some important applications in continuum mechanics and elasticity theory [15,16,17,18,19,20,21,22,23], the oscillatory behavior of the solutions of fourth-order differential equations with p-Laplacian like operator have been investigated in recent years by using different methods and various techniques, for example, [24,25,26]
Let xðtÞ be a positive and n -times differentiable function on an 1⁄2T, ∞Þ with its nth derivative xðnÞðtÞ nonpositive on 1⁄2T, ∞Þ and not identically zero on Journal of Function Spaces any interval of the form 1⁄2T ′, ∞Þ, T ′ ≥ T
Summary
We are concerned with the oscillation behavior of solutions of the fourth-order p-Laplacian differential equations with middle term rðtÞz. The p-Laplacian differential equations there are some important applications in continuum mechanics and elasticity theory [15,16,17,18,19,20,21,22,23], the oscillatory behavior of the solutions of fourth-order differential equations with p-Laplacian like operator have been investigated in recent years by using different methods and various techniques, for example, [24,25,26].
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