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On positive solutions of fourth order nonlinear differential inequalities

  • Manabu Naito
Article

Summary

This paper is concerned with positive solutions of the fourth order nonlinear differential inequality
$$\left( {r_3 \left( t \right)\left( {r_2 \left( t \right)\left( {r_1 \left( t \right)x'} \right)'} \right)'} \right)' + f\left( {x,t} \right)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } 0, t\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } a.$$
(A)
Necessary and sufficient conditions are presented for the existence of special types of positive solutions of(A). When r 1 (t) ≡ r 3 (t), necessary and sufficient conditions are established for the existence of positive solutions of(A) which is either strongly superlinear or strongly sublinear.

Keywords

Fourth Order Differential Inequality Nonlinear Differential Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Nicola Zanichelli Editore 1978

Authors and Affiliations

  • Manabu Naito
    • 1
  1. 1.HiroshimaJapan

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