Affiliation:
1. Institut de Mathématique Pure et Appliquée Université Catholique de Louvain Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgique
2. Dipartimento di Scienze Matematiche Università degli Studi di Trieste Via A. Valerio 12/1, I-34127 Trieste, Italia
Abstract
Abstract
The existence of positive solutions is proved for the prescribed mean curvature problem
where Ω ⊂ℝN is a bounded smooth domain, not necessarily radially symmetric. We assume that ∫0
u f(x, s) ds is locally subquadratic at 0, ∫0
u g(x, s) ds is superquadratic at 0 and λ > 0 is sufficiently small. A multiplicity result is also obtained, when ∫0
u f(x, s) ds has an oscillatory behaviour near 0. We allow f and g to change sign in any neighbourhood of 0.
Subject
General Mathematics,Statistical and Nonlinear Physics
Reference13 articles.
1. On the existence of positive solutions of semilinear elliptic equations;Lions;SIAM Review,1982
2. A barrier method for mean curvature prob - lems Nonlinear;Noussair;Anal,1993
3. Combined effects of concave and convex non - linearities in some elliptic problems Functional;Ambrosetti;Anal,1994
4. Positive solutions of the prescribed mean curvature equation in RN Indiana;Noussair;Univ Math,1993
5. de Figueiredo Local superlinearity and sublinearity for indefinite semilinear elliptic problems Functional;Gossez;Anal,2003
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