Positivity results for indefinite sublinear elliptic problems via a continuity argument

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Kaufmann, U.¹  Ramos Quoirin, H.²  Umezu, K.³ 

[1] Univ Nacl Cordoba, FAMAF, RA-5000 Cordoba, Argentina

[2] Univ Santiago Chile, Casino 307,Correo 2, Santiago, Chile

[3] Ibaraki Univ, Dept Math, Fac Educ, Mito, Ibaraki 3108512, Japan

关键词: Elliptic problem;    Indefinite;    Sublinear;    Positive solution;   

DOI  :  10.1016/j.jde.2017.05.021

来源: Elsevier

【 摘 要 】

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free