[PDF] Top 20 Construction of lower and upper solutions for first-order periodic problem

... Lemma . If problem (.) has a lower solution α and upper solution β such that α(t) ≤ β (t) for all t ∈ [, T] (resp. β(t) ≤ α(t) for all t ∈ [, T ]), then problem (.) has at least one ... See full document

... we first develop the method of generalized quasilinearization for initial value problem of an integro differential equation and then use it to develop quasilinearization for the periodic boundary ... See full document

... of first order impulsive integro-differential equations with multi-point boundary ...of lower and upper solutions in reversed order coupled with the monotone iterative technique, ... See full document

... of order 0 < α ≤ ...of lower and upper solutions coupled with the monotone iterative technique, we construct two monotone iterative sequences and prove that the sequences monotonically ... See full document

... coupled lower and upper solutions we develop the generalized monotone iterative technique to solve Caputo fractional integro-differential equation of order q with periodic boundary ... See full document

... on periodic solutions for ordinary differential equations is a very important branch in the differential equation ...of periodic solutions for second-order differential equations have been ... See full document

... value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the ... See full document

... of upper-lower solutions must be ...of upper-lower solutions for concrete functional differential ...positive periodic solutions for four-point fractional ... See full document

... for problem (1) and (2), we use the method of lower and upper solutions coupled with the monotone iterative ...of lower and upper solutions is not perfect, for example, in ... See full document

... the upper and lower solution method together with the iterative technique is a powerful tool for proving the existence results for boundary value problems (see [–] and the references ...the upper ... See full document

... of problem (P) if it satisfies equation (P) in N and u(n) = u(N + n) for all n ∈ N ...its first variable, it is obvious that to look for an N -periodic solution of (P) is equivalent to solve ... See full document

...        uniformly in v V  . (3.24) Hence by Lemma 3.1 and properties (3.18), (3.24), we deduce that the functional  satisfies all the assump- tions of Theorem 2.1. Therefore the Hamiltonian system (࣢) possesses ... See full document

... the upper or lower solutions of the ...an upper (or lower) solution sequence which then converges to the solution ...of upper and lower solutions as two initial ... See full document

... The rest of the paper is organized as follows: In Section , we state some notations and preliminary results. Sections  and  are devoted to study the bifurcation from infinity and from the trivial solution for a ... See full document

... the parameters of (1.1) can be found in [1, 2]. It is well known that the variation of the envi- ronment plays an important role in many biological and ecological dynamical systems. In particular, periodically varying ... See full document

... It is easy to see that in either equation (1.3) or the equation in problem (1.4)–(1.5), the singular terms are all autonomous. Despite the fact that there are many papers focusing on the equation with ... See full document

... a periodic solution of nonautonomous differential equations,” Differentsial’nye Uravneniya, ...“On periodic solutions of even-order ordinary differential ... See full document

... Fractional order differential equations have a wide range of applications in various fields of science and engineering such as physics, fluid flows, flow in porous media, electrical networks and ...via lower and ... See full document

... bounded solutions to the linear first-order difference equation on the set of all integers is ...of solutions converging to zero when n → – ∞ , as well as when n → + ∞ , are also ...are ... See full document

... where G(t, s) is the Green’s function associated to (1.2), see [7–13] for more details. Compared with the non-resonant problems, the research of resonant problems proceeds very slowly and the related results are few. ... See full document