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Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population

100%
Amar A.
Open Mathematics
|
2011
|
tom 9
|
nr 4
851-865
EN
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
2
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Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

100%
Amar A.
Open Mathematics
|
2013
|
tom 11
|
nr 1
85-93
EN
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
3
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Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

88%
Jessada T., Ntouyas S. K., Asawasamrit S., Promsakon C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
645-666
EN
In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.
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