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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

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.

Layer potentials C*-algebras of domains with conical points

81%

Carvalho C., Qiao Y.

Open Mathematics

2013

tom 11

nr 1

27-54

To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm conditions for the natural pseudodifferential operators affiliated to this C*-algebra.

Ograniczanie wyników

2 Open Mathematics

1 Amar A.

1 Carvalho C.

1 Qiao Y.

1 2013

1 2011

Wyniki wyszukiwania

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

Layer potentials C*-algebras of domains with conical points