The elliptic equations with deviated arguments appear in some models of population such as in biology, etc. as indicated in the books [4] and [5] and the works of Levin [3], Skellam [6]. In this paper, we establish some results of existence and uniqueness for some non-local equations called elliptic equations with deviated argument. Firstly, we handle linear and nonlinear cases. Therefore, we hope to complete some results obtained by Chipot and Mardare [2].
Les équations elliptiques à arguments déviés apparaissent dans certains modèles de population, en biologie, etc., comme il est indiqué dans les ouvrages [4] et [5] et dans les travaux de Levin [3] et de Skellam [6]. Nous établissons dans ce papier quelques résultats dʼexistence et dʼunicité pour certaines équations elliptiques non-locales dites à argument dévié. Nous traitons dʼabord des cas linéaires puis des cas non-linéaires. Nous espérons ainsi compléter certains résultats obtenus par Chipot et Mardare [2].
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Anouar Houmia 1, 2
@article{CRMATH_2014__352_2_113_0, author = {Anouar Houmia}, title = {\'Etude de certaines \'equations elliptiques \`a argument d\'evi\'e}, journal = {Comptes Rendus. Math\'ematique}, pages = {113--116}, publisher = {Elsevier}, volume = {352}, number = {2}, year = {2014}, doi = {10.1016/j.crma.2013.11.021}, language = {fr}, }
Anouar Houmia. Étude de certaines équations elliptiques à argument dévié. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 113-116. doi : 10.1016/j.crma.2013.11.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.021/
[1] The diffusion of a population partly driven by its preferences, Arch. Ration. Mech. Anal., Volume 155 (2000), pp. 237-259
[2] On a model of diffusion of population, Int. J. Dyn. Syst. Differ. Equ., Volume 1 (2008) no. 3, pp. 177-190
[3] Spatial patterning and the structure of ecological communities (S.A. Levin, ed.), Some Mathematical Questions in Biology, 7, Lectures on Mathematics in the Life Sciences, vol. 8, Amer. Math. Soc., Providence, RI, 1976, pp. 1-35
[4] Mathematical Biology, Springer, 1993
[5] Diffusion and Ecological Problems:Mathematical Models, Springer, 1980
[6] Random dispersial in theoretical populations, Biometrika, Volume 38 (1951), pp. 196-218
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