On a class of nonlocal nonlinear elliptic problems

Abstract

On a class of nonlocal nonlinear elliptic problems RAIRO-Modélisation mathématique et analyse numérique, tome 26, n o 3 (1992), p. 447-467. <http://www.numdam.org/item?id=M2AN_1992__26_3_447_0> © AFCET, 1992, tous droits réservés. L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ [X] MATHEMATICALMOOEUJHGAHDHUMERICALAHALYSIS MOMUSATIOH MATHÉMATIQUE ET ANALYSE NUMÉRIQUE

On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method

“…In case q = 2, we get the well-known Carrier equation which is an appropriate model to study some questions related to nonlinear deflections of beams. See [4][5][6][7]10] and the references therein, for more details related to problem (1.4).…”

An optimal control problem for a Kirchhoff-type equation

“…Nonlocal problems start out in the papers of Kirchhoff, [8], where he introduced his celebrated equation There are a relevant range of situations in Physics and Technology where problems with nonlocal terms appear, see for instance [1,2,4,10,14] and the survey [13]. In this paper we study an optimal control problem associated to (1.2) in the particular case M (x, r) = a(x)+b(x)r where a(x), b(x) are positive continuous functions.…”

On doubly nonlocal fractional elliptic equations

“…As is well-known, nonlocal Laplacian boundary value problems model several physical and biological systems where u describes a process which depends on the average of itself, for example, the population density (see [1,4,13,14,34]). In the vast literature on this subject, we also refer the reader to some interesting results obtained by Autuori and Pucci in [5,6,7]studying Kirchhoff equations by using different approaches.…”