[PDF] Top 20 Notes on the Solutions of the First Order Quasilinear Differential Equations

... (1,2,3)-nontrivial solutions x(t) of systems of two (three) first order quasi- linear differential equations have been investigated by Mamrilla, ...(t) solutions of the systems, ... See full document

... (in Theorems , , ) can be expanded to some non-linear functional differential equations (see Remark ). Theorem  gives the best possible estimates of the norm of the Green oper- ator for the periodic boundary ... See full document

... x (t) = − x(t − 1) for a.a. t ∈ [0, 1], x(t) = k(t) = − t for t ∈ [ − 1, 0]. (9) Notice that functions a(t) = 0 and b(t) = 1, t Î [-1, 1], are lower and upper solutions in the usual sense for problem (9). However, ... See full document

... for all t ∈ I respectively. Clearly, C(I; R ) is a Banach algebra with respect to above supremum norm and is also partially ordered w.r.t. the above partially order relation ≤. It is known that the partially ... See full document

... upper solutions is good in practice, but once we have found them we can immediately construct a pair of continuous lower and upper solutions which provide better information on the location of the ... See full document

... of our knowledge, there are few papers published on positive almost periodic solutions of (1.1) and (1.2). Motivated by the above discussions, in this paper we aim to establish some sufficient conditions on the ... See full document

... positive solutions to problems of type ...positive solutions have been investigated for such general boundary value problems with functionals λ  , λ  and with deviating arguments α, β in differential ... See full document

... R is a not necessarily continuous function, satisfying some assumptions to be detailed. Finally, F : C(I) −→ R is assumed to be continuous, but not necessarily linear or bounded. Notice that, under this framework, ... See full document

... 1. Browder, F: A further generalization of the Schauder fixed-point theorem. Duke Math. J. 32, 575-578 (1965) 2. Grafton, RB: A periodicity theorem for autonomous functional differential equations. J. Differ. Equ. 6, ... See full document

... periodic solutions for problem ...periodic solutions for problem ...periodic solutions and the dependence results of the positive periodic solution on the parameter when the function g satisfies ... See full document

... differential equations arise in a variety of different areas of applied mathematics and ...differential equations was initiated by Il’in and Moiseev 1, ...positive solutions for differential ... See full document

... There are no proofs in these first chapters. All results are referenced from textbooks and papers. The focus of this thesis is describing the arguments of [8]. In chapter 4 we state the problem of existence and ... See full document

... weak solutions when b(x) and f (u) satisfy some suitable conditions, which are different from the conditions in our ...p-Laplacian equations, we refer to [–] and references ... See full document

... and to conclude that (5.19) has the same oscillatory behavior as (5.16). Since (5.15) holds, applying another comparison principle, Theorem 5.1, we conclude that all the solutions of (A) are necessarily ... See full document

... In this paper, we study a class of first-order neutral differential equations with time-varying delays and coefficients. Employing the fixed point method and differential inequality techniques, easily verifiable ... See full document

... 2. Preliminary results. We prove a sequence of lemmas which are needed in order to prove our main result. To illustrate the general results obtained for the problem in (1.5), (1.6), we from time to time consider ... See full document

... Numerical Solutions of a Fuzzy Initial Value Problem Consider the first order Fuzzy Initial Value Problem ...the first order term of the Taylor series to find an approximate solution of ... See full document

... positive solutions of second order quasilinear ordinary differential equations (p(t) ϕ (x (t))) + q(t) ψ (x(t)) = 0 are studied in the framework of regular variation, where p and q are ... See full document

... of solutions for various kinds of neutral delay differential equations has attracted much ...of solutions which are bounded by positive constants, ... See full document

... Differential equations involving impul- sive effects occur in many applications: physics, population dynamics, ecology, biological systems, biotechnology, industrial robotic, pharmacokinetics, optimal control, ... See full document