Displaying similar documents to “Oscillation and spectral properties of self-adjoint even order differential operators with middle terms.”

Oscillation and nonoscillation of higher order self-adjoint differential equations

Ondřej Došlý, Jan Osička (2002)

Czechoslovak Mathematical Journal

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Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation ( - 1 ) n ( t α y ( n ) ) ( n ) + q ( t ) y = 0 ( * ) are established. In these criteria, equation ( * ) is viewed as a perturbation of the conditionally oscillatory equation ( - 1 ) n ( t α y ( n ) ) ( n ) - μ n , α t 2 n - α y = 0 , where μ n , α is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.

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.