TY  - JOUR
ID  - Graef2023
LB  - Graef2023
AU  - Graef, John R.
AU  - Hebboul, Doudja
AU  - Moussaoui, Toufik
TI  - Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball
ST  - Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 1
SP  - 47
EP  - 66
DO  - https://doi.org/10.7494/OpMath.2023.43.1.47
UR  - https://doi.org/10.7494/OpMath.2023.43.1.47
AB  - In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the \(p\)-Laplacian \[-\Big(a+b\int_{\Omega_e}|\nabla u|^p dx\Big)\Delta_p u=\lambda f\left(|x|,u\right),\ x\in \Omega_e,\quad u=0\ \text{on} \ \partial\Omega_e,\] where \(\lambda \gt 0\) is a parameter, \(\Omega_e = \lbrace x\in\mathbb{R}^N : |x|\gt r_0\rbrace\), \(r_0\gt 0\), \(N \gt p \gt 1\), \(\Delta_p\) is the \(p\)-Laplacian operator, and \(f\in C(\left[ r_0, +\infty\right)\times\left[0,+\infty\right),\mathbb{R})\) is a non-decreasing function with respect to its second variable. By using the Mountain Pass Theorem, they prove the existence of positive radial solutions for small values of \(\lambda\).
KW  - Kirchhoff problem
KW  - \(p\)-Laplacian
KW  - positive radial solution
KW  - variational methods
SN  - 1232-9274
ER  -