Electron. J. Differential Equations, Vol. 2017 (2017), No. 185, pp. 1-9.

Existence of solutions to (2,p)-Laplacian equations by Morse theory

Zhanping Liang, Yuanmin Song, Jiabao Su

Abstract:
In this article, we use Morse theory to investigate a type of Dirichlet boundary value problem related to the (2,p)-Laplacian operator, where the nonlinear term is characterized by the first eigenvalue of the Laplace operator. The investigation is heavily based on a new decomposition about the Banach space $W^{1,p}_0(\Omega)$, where $\Omega\subset \mathbb{R}^N\; (N\geq 1)$ is a bounded domain with smooth enough boundary.

Submitted September 26, 2016. Published July 21, 2017.
Math Subject Classifications: 35J50, 35J92, 58E05.
Key Words: (2,p)-Laplacian equation; Morse theory.

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Zhanping Liang
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, Shanxi, China
email: lzp@sxu.edu.cn
  Yuanmin Song
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, Shanxi, China
email: 954126769@qq.com
  Jiabao Su
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: sujb@cnu.edu.cn

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