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Methods of oscillation theory of half-linear second order differential equations

Ondřej Došlý — 2000

Czechoslovak Mathematical Journal

In this paper we investigate oscillatory properties of the second order half-linear equation ( r ( t ) Φ ( y ' ) ) ' + c ( t ) Φ ( y ) = 0 , Φ ( s ) : = | s | p - 2 s . ( * ) Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.

Qualitative theory of half-linear second order differential equations

Ondřej Došlý — 2002

Mathematica Bohemica

Some recent results concerning properties of solutions of the half-linear second order differential equation ( r ( t ) Φ ( x ' ) ) ' + c ( t ) Φ ( x ) = 0 , Φ ( x ) : = | x | p - 2 x , p > 1 , ( * ) are presented. A particular attention is paid to the oscillation theory of ( * ) . Related problems are also discussed.

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