Existence of solutions for Kirchhoff-type problems via the method of lower and upper solutions

• Main Authors: Baoqiang Yan, Donal O'Regan, Ravi P. Agarwal
• Format: Article
• Language: English
• Published: Texas State University 2019-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Kirchhoff-type elliptic problem; lower and upper solution; topological degree
• Online Access: http://ejde.math.txstate.edu/Volumes/2019/54/abstr.html

This article considers elliptic problems of Kirchhoff-type. We give some new definitions of lower and upper solutions for the problem and establish the method of lower and upper solutions when the upper and lower solutions are well ordered, i.e., the lower solution is less than the upper one, and we also consider the case when the upper and lower solutions have opposite ordering. In addition we use the relation between the topological degree and strict upper and lower solutions in both cases and using this we obtain multiplicity results for nonlinear Kirchhoff-type elliptic problems.