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
The monotone method for periodic differential equations with the non well-ordered upper and lower solutions
β Scribed by Aijun Yang; Weigao Ge
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 465 KB
- Volume
- 232
- Category
- Article
- ISSN
- 0377-0427
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β¦ 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.
π SIMILAR VOLUMES
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 ;,
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.
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