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On asymptotic decaying solutions for a class of second order differential equations

Serena Matucci (1999)

Archivum Mathematicum

The author considers the quasilinear differential equations r ( t ) ϕ ( x ' ) ' + q ( t ) f ( x ) = 0 , t a and r ( t ) ϕ ( x ' ) ' + F ( t , x ) = ± g ( t ) , t a . By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.

On bounded nonoscillatory solutions of third-order nonlinear differential equations

Ivan Mojsej, Alena Tartaľová (2009)

Open Mathematics

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.

On L w 2 -quasi-derivatives for solutions of perturbed general quasi-differential equations

Sobhy El-sayed Ibrahim (1999)

Czechoslovak Mathematical Journal

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of n th order with complex coefficients M [ y ] - λ w y = w f ( t , y [ 0 ] , ... , y [ n - 1 ] ) , t [ a , b ) provided that all r th quasi-derivatives of solutions of M [ y ] - λ w y = 0 and all solutions of its normal adjoint M + [ z ] - λ ¯ w z = 0 are in L w 2 ( a , b ) and under suitable conditions on the function f .

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