Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 87, pp. 1-20.

Title: Existence of infinitely many solutions of p-Laplacian equations in R^N+

Authors: Junfang Zhao (China Univ. of Geosciences, Beijing, China)
         Xiangqing Liu (Yunnan Normal Univ., Kunming, China)
         Jiaquan Liu (Peking Univ., Beijing, China)
 
Abstract:
 In this article, we study the p-Laplacian equation
 $$\displaylines{
 -\Delta_p u=0, \quad \text{in }  \mathbb{R}^N_{+},\cr
 |\nabla u|^{p-2}\frac{\partial u}{\partial n}+a(y)|u|^{p-2}u=|u|^{q-2}u , \quad
 \text{on } \partial\mathbb{R}^N_{+}=\mathbb{R}^{N-1},
 }$$
 where $1<p<N$, $p<q<\bar{p}=\frac{(N-1)p}{N-p}$,
 $\Delta_p=$div$(|\nabla u|^{p-2}\nabla u)$  the p-Laplacian operator,
 and the positive, finite function a(y) satisfies suitable decay
 assumptions at infinity. By using the truncation method, we prove the
 existence of infinitely many solutions.

Submitted September 22, 2018. Published July 16, 2019.
Math Subject Classifications: 35B05, 35B45.
Key Words: p-Lalacian equation; half space; boundary value problem; 
           multiple solutions; truncation method.