A discontinuous functional differential equation

Pikuta, Piotr; Rzymowski, Witold

doi:10.1016/s0022-247x(02)00510-3

Cited by 5 publications

(7 citation statements)

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“…[5]). Some simpler cases of the problem have been considered in [6][7][8][9], where the corresponding existence of local solution was investigated. Clearly, in order that (5.1) + (5.2) has a solution, one must necessarily have the compatibility condition .0/ D .0/.…”

Section: Proofmentioning

confidence: 99%

“…Several special cases of the problem have been considered in [6][7][8][9], where the corresponding existence of local (not global) solution was investigated. The commonly used methods to treat the existence of local solutions for Darboux problems involve functional differential equations and method of upper and lower solutions based on Schauder's fixed-point theorem (see [8][9][10][11] and the references therein). Because of the unboundedness of the domain, the existence of global solution to the Darboux problem (1.2) + (1.3) is not easy to obtain and has been rarely studied.…”

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confidence: 99%

“…8) where > 0, a and b satisfy (H1), satisfies .H3/, and f satisfies (H5) f : R ! R, jf .u/j Ä Q for every u 2 R andjf .u/ f .v/j Ä d 4 ju vj, 8u, v 2 R…”

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confidence: 99%

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Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Xiang

Georgiev

2015

Math Methods in App Sciences

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Communicated by W. SprößigIn this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations.

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Section: Proofmentioning

confidence: 99%

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confidence: 99%

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Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Xiang

Georgiev

2015

Math Methods in App Sciences

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“…Our motivation is to improve in a unified way the main results in the recent papers [3], [6,20] and [25].…”

Section:  Z (T) = G(t Z(t)) For Aa T ∈ [0 T ]mentioning

confidence: 99%

On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations

Cid

2005

Proc. Amer. Math. Soc.

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“…Although the main purpose of this paper is to establish an existence theorem for (1)-(2), the method used here, see also see [7] involves functional differential equations, namely, we deal with the problem…”

Section: Introductionmentioning

confidence: 99%