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Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball

Graef John R., Hebboul Doudja, Moussaoui Toufik

Opuscula Mathematica

2023

Vol. 43, no. 1

47--66

In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the p-Laplacian [formula] where λ > 0 is a parameter, Ωe = {x ∈ RN : |x| > r0}, r0 > 0, N > p > 1, Δp is the p-Laplacian operator, and f ∈ C([r0,+∞) × [0,+∞) ,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 λ.