Displaying similar documents to “Limit and integral properties of principal solutions for half-linear differential equations”

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.

Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations

Luisa Malaguti, Valentina Taddei (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the quasi-linear ordinary differential equation ( r ( t ) ϕ ( u ' ) ) ' + g ( t , u ) = 0 with t [ 0 , ) . We treat the case when g is not necessarily monotone in its second argument and assume usual conditions on r ( t ) and ϕ ( u ) . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano,...

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.