Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition

Abstract

We study the degenerate elliptic equation ▫$$ -\operatorname{div}(|x|^\alpha \nabla u) = f(u) + t\phi(x) + h(x)$$▫ in a bounded open set ▫$\Omega$▫ with homogeneous Neumann boundary condition, where ▫$\alpha \in (0,2)$▫ and ▫$f$▫ has a linear growth. The main result establishes the existence of real numbers and ▫$t^\ast$▫ such that the problem has at least two solutions if ▫$t \leq t_\ast$▫, there is at least one solution if ▫$t_\ast < t \leq t^\ast$▫, and no solution exists for all ▫$t > t^\ast$▫. The proof combines a priori estimates with topological degree arguments.

Keywords

Ambrosetti-Prodi problem;degenerate potential;topological degree;anisotropic continuous media;

Data

Language:	English
Year of publishing:	2018
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	18249305
ISSN:	1072-6691
Views:	421
Downloads:	103
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. no. 41, str. 1-10
Issue:	ǂVol. ǂ2018
Chronology:	2018
ID:	11214239