A Neumann problem of Ambrosetti-Prodi type

Author(s)

Presoto, Adilson Eduardo ^[1] ; de Paiva, Francisco Odair ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Fixed Point Theory and Applications; v. 18, n. 1, p. 189-200, MAR 2016.
• Web of Science Citations: 5

Abstract

The aim of this paper is to establish an Ambrosetti-Prodi-type result for the problem [-Delta u = g(x, u, del u) + t phi in Omega, partial derivative u/partial derivative eta = 0 on partial derivative Omega; i.e., under appropriate conditions, we will show that there exists a constant t(0) such that the problem above has no solution if t > t(0), at least a solution if t = t(0) and at least two solutions if t < t(0). The proof is based on a combination of upper and lower solutions method and the Leray-Schauder degree. (AU)

• FAPESP's process: 14/18556-8 - Elliptic problems by variational and topological methods
• Grantee: Francisco Odair Vieira de Paiva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/20831-7 - Semilinear elliptic problems
• Grantee: Adilson Eduardo Presoto
• Support Opportunities: Regular Research Grants