Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 42, pp. 1-12.

Title: Existence and multiplicity of solutions for non-degenerate
       Kirchhoff type problem with nonlinear boundary condition

Authors: Mateus Balbino Guimaraes
         Elard Juarez Hurtado
         Rodrigo da Silva Rodrigues
 
Abstract:
 We show the existence of solutions for nonlinear elliptic partial differential
 equations with Steklov nonlinear boundary conditions involving a Kirchhoff 
 type operator.  By using variational and topological methods, we prove the 
 existence and multiplicity of solutions.  The results obtained are new even 
 for the standard stationary Kirchhoff equation with nonlinear
 boundary condition involving the p-Laplacian operator.


Submitted May 25, 2018. Published March 22, 2019.
Math Subject Classifications: 35A15, 35J60.
Key Words: Variational methods; nonlinear elliptic equations;
           Steklov-Neumann eigenvalues.