Work

A loop type component in the non-negative solutions set of an indefinite elliptic problem

Year: 2018

Type: article

Abstract: We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with a homogeneous Neumann boundary condition. This result complements our previous results obtained in [12], where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory, rescaling and regularizing arguments, a priori bounds, and Whyburn's topological method. A further investigation of the loop type component established in [12] is also provided.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2018060

Authors: Humberto Ramos Quoirin, Kenichiro Umezu

Institution: Ibaraki University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: Study on the bifurcation structure of positive solutions for concave-convex mixed nonlinear elliptic boundary value problems with indefinite weights