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On property (B) of higher order delay differential equations

Blanka Baculíková, Jozef Džurina (2012)

Archivum Mathematicum

In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the n -th order delay differential equations ( r ( t ) [ x ( n - 1 ) ( t ) ] γ ) ' = q ( t ) f ( x ( τ ( t ) ) ) . Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases r - 1 / γ ( t ) t = and r - 1 / γ ( t ) t < are discussed.

On some boundary value problems for second order nonlinear differential equations

Zuzana Došlá, Mauro Marini, Serena Matucci (2012)

Mathematica Bohemica

We investigate two boundary value problems for the second order differential equation with p -Laplacian ( a ( t ) Φ p ( x ' ) ) ' = b ( t ) F ( x ) , t I = [ 0 , ) , where a , b are continuous positive functions on I . We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: i ) x ( 0 ) = c > 0 , lim t x ( t ) = 0 ; ii ) x ' ( 0 ) = d < 0 , lim t x ( t ) = 0 .

Currently displaying 81 – 100 of 324