Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 54, pp. 1-19.

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

Authors: Baoqiang Yan (Shandong Normal Univ., Jinan, China)
         Donal O'Regan (National Univ. of Ireland, Galway, Ireland)
         Ravi P. Agarwal (Texas A and M Univ., Kingsville, Texas, USA)

Abstract:
 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.

Submitted January 31, 2019. Published April 29, 2019.
Math Subject Classifications: 35J60, 35J75, 47H10.
Key Words: Kirchhoff-type elliptic problem; lower and upper solution; 
           topological degree.