EconPapers    
Economics at your fingertips  
 

Existence, Uniqueness and C −Differentiability of Solutions in a Non-linear Model of Cancerous Tumor

Gossan D. Pascal Gershom, Yoro Gozo and Bailly Bal´e

Journal of Mathematics Research, 2018, vol. 10, issue 6, 43-62

Abstract: In this paper, we prove the existence and uniqueness of the weak solution of a system of nonlinear equations involved in the mathematical modeling of cancer tumor growth with a non homogeneous divergence condition. We also present a new concept of generalized differentiation of non linear operators : C −differentiability. Through this notion, we also prove the uniqueness and the C −differentiability of the solution when the system is perturbed by a certain number of parameters. Two results have been established. In the first one, differentiability is according to Fr´echet. The proof is given uses the theorem of reciprocal functions in Banach spaces. First of all, we give the proof of strict differentiability of a direct mapping, according to Fr´echet. In the second result, differentiability is understood in a weaker sense than that of Fr´echet. For the proof we use Hadamard’s theorem of small perturbations of Banach isomorphism of spaces as well as the notion of strict differentiability.

Keywords: cancer; existence; uniqueness and C −differentiability; weak solution; perturbed system; isomorphism (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/37230/37449 (application/pdf)
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/37230 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:43

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education (jmr@ccsenet.org).

 
Page updated 2024-12-28
Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:43