[PDF] Top 20 Limit Properties of Solutions of Singular Second-Order Differential Equations

... To illustrate the solution behaviour, described by Theorems 3.3 and 3.5, we have carried out a series of numerical calculations on a MATLAB software package bvpsuite designed to solve boundary value problems in ordinary ... See full document

... qualitative properties of solutions to ODEs of second order, fixed point method, perturbation theory, variations of parameters formulas, the Lyapunov second method, and so on have been ... See full document

... In 2002, Chen [3] considered the question: What conditions on B(z) when ρ(B) = 1 will guarantee that every nontrivial solution of (1.1) has infinite order? He proved the following result, which improved results of ... See full document

... where a min{0, inf{τ t : 0 ≤ t ≤ 1}}, b max{1, sup{τt : 0 ≤ t ≤ 1}}, and the existence of positive solutions to 1.1 is obtained. When τt t − r in 1.1, Agarwal and O’Regan in 5, Lin and Xu in 6 discussed the ... See full document

... periodic solutions do not ...periodic solutions under the presence of a weak singularity by topological methods is more recent but has also attracted many researchers 4, 6, ...lower solutions 6, 29, ... See full document

... the properties of the Weyl matrix disks, Sun [] established the Weyl-Titchmarsh theory of Hamiltonian systems on time ...the second-order singular differential and difference equations ... See full document

... differential equations have been randomized and rigorously studied in [3, 4, 7, 8, 10], ...differential equations it is well known that they admit polynomial solutions, in those contributions the ... See full document

... of solutions for some second-order boundary value problem with impulsive effects on an unbounded ...positive solutions for singular Sturm- Liouville boundary value problems for ... See full document

... differential equations has been emerging as an important area of investigation in recent years (see ...differential equations, impulsive functional differential equations and impulsive differential ...of ... See full document

... As mentioned above, this paper is mainly motivated by the recent paper [, ]. The aim of this paper is to study the multiplicity of positive solutions to (.). It is proved that such a problem has at least two ... See full document

... Clearly, the constant function ut ≡ L is a solution of problem 1.1, 1.2. An important question is the existence of a strictly increasing solution of 1.1, 1.2 because if such a solution exists, many important physical ... See full document

... has exactly k zeros in (a,b), it is possible to obtain the asymptotic distribution of eigen- values from the asymptotic number of zeros of solutions, an idea which goes back at least to Hartman (see [3]). For the ... See full document

... periodic solutions to second order differential equations with singular nonlinear ...positive solutions under reasonable ... See full document

... Remark  A closer examination of the proof of Theorem  shows that the condition lim u→+ | ˆ F(u)| = ∞ is somehow needed. Indeed, if we assume that this limit is finite and that a ∞ H(s) ds = ∞, then in view of ... See full document

... The purpose of this paper is to investigate further the singular BVP for delay higher- order dynamic equation 1.1. By the use of the fixed point theorem of cone expansion and compression type, results on ... See full document

... In all the above-mentioned works, differential equations and systems, not having singu- larities in phase variables, are considered. The Kneser problem for the differential equa- tion with a singularity in one of ... See full document

... In applied science, some practical problems such as nonlinear oscillations [, ], fluid me- chanical and nonlinear elastic mechanical phenomena [–] are associated with the peri- odic solutions of nonlinear ... See full document

... meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f 00 + Af 0 + Bf = F, where A (z) , B (z) and F (z) are meromorphic functions with ... See full document

... Oscillation, Nonoscillation and Growth of Solutions of Nonlinear Functional Differential Equations of Arbitrary Order, J.. Asymptotic Properties of Solutions of Functional Differential E[r] ... See full document

... the order of growth of a meromorphic function f (z), λ(f ) to denote the exponents of convergence of the zero- sequence of a meromorphic function f (z), λ(f ) to denote the exponents of convergence of the sequence ... See full document