On the Ambrosetti–Prodi Problem for Non-Variational Elliptic Systems [chapter]

Djairo G. de Figueiredo, Boyan Sirakov
2007 Djairo G. de Figueiredo - Selected Papers  
We study the Ambrosetti-Prodi problem for nonlinear elliptic equations and systems, with uniformly elliptic operators in non-divergence form and non-smooth coefficients, and with nonlinearities with linear or power growth. 1 Problem (1) is said to be of Ambrosetti-Prodi type provided there exist constants a, b, C such that b > λ 1 > a, and for all x ∈ Ω, This hypothesis is equivalent to the existence of constants a , b such that lim sup A typical result in this setting states (AP) There exists
more » ... (AP) There exists t 0 ∈ R such that problem (1) has at least two solutions for t < t 0 , at least one solution for t = t 0 , and no solutions for t > t 0 .
doi:10.1007/978-3-319-02856-9_39 fatcat:srkpt6czljeoxaw5nolbs5i4xq