On oscillatory solutions of third-order linear differential equations
In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the -th order delay differential equations 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 and are discussed.
We investigate two boundary value problems for the second order differential equation with -Laplacian where , are continuous positive functions on . 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: