𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The monotone method for periodic differential equations with the non well-ordered upper and lower solutions

✍ Scribed by Aijun Yang; Weigao Ge


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
465 KB
Volume
232
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis


In this paper, we consider the following periodic problem:

The unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal, in which case they are the expected unique solution.


πŸ“œ SIMILAR VOLUMES


The monotone method for Neumann function
✍ Daqing Jiang; Ying Yang; Jifeng Chu; Donal O’Regan πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 277 KB

In this paper, we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and Ο†-Laplacian equations with Neumann boundary value conditions. Moreover, we obtain existence results assuming upper an

Unstable Periodic Solutions of a Parabol
✍ Colette De Coster; Pierpaolo Omari πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 243 KB

We prove the solvability of the Dirichlet-periodic problem for a semilinear parabolic equation, assuming the existence of a lower solution : and an upper solution ;, which do not satisfy the ordering condition : ;. Our results yield the existence of unstable solutions, localized by means of : and ;,

Upper and lower solutions method for imp
✍ SaΓ―d Abbas; Mouffak Benchohra πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier 🌐 English βš– 273 KB

In this paper we investigate the existence of solutions for a class of initial value problems for impulsive partial hyperbolic differential equations involving the Caputo fractional derivative by using the lower and upper solutions method combined with Schauder's fixed point theorem.

Extremal solutions for the first order i
✍ Guotao Wang; Lihong Zhang; Guangxing Song πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 300 KB

boundary conditions a b s t r a c t This paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence of solutions by establishing a new comparison princip