Displaying similar documents to “On the asymptotic nature of a class of second order nonlinear systems.”

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

Ondřej Došlý (2000)

Czechoslovak Mathematical Journal

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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

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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.

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska (2007)

Open Mathematics

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The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.