Translator Disclaimer
February, 2019 Two Positive Solutions for Kirchhoff Type Problems with Hardy-Sobolev Critical Exponent and Singular Nonlinearities
Yu-Ting Tang, Jia-Feng Liao, Chun-Lei Tang
Taiwanese J. Math. 23(1): 231-253 (February, 2019). DOI: 10.11650/tjm/180705

Abstract

We consider the following singular Kirchhoff type equation with Hardy-Sobolev critical exponent \[ \begin{cases} \displaystyle -\left( a + b \int_{\Omega} |\nabla u|^2 \, dx \right) \Delta u = \frac{u^{3}}{|x|} + \frac{\lambda}{|x|^{\beta} u^{\gamma}}, & x \in \Omega, \\ u > 0, & x \in \Omega, \\ u = 0, & x \in \partial \Omega, \end{cases} \] where $\Omega \subset \mathbb{R}^{3}$ is a bounded domain with smooth boundary $\partial \Omega$, $0 \in \Omega$, $a,b,\lambda \gt 0$, $0 \lt \gamma \lt 1$, and $0 \leq \beta \lt (5+\gamma)/2$. Combining with the variational method and perturbation method, two positive solutions of the equation are obtained.

Citation

Download Citation

Yu-Ting Tang. Jia-Feng Liao. Chun-Lei Tang. "Two Positive Solutions for Kirchhoff Type Problems with Hardy-Sobolev Critical Exponent and Singular Nonlinearities." Taiwanese J. Math. 23 (1) 231 - 253, February, 2019. https://doi.org/10.11650/tjm/180705

Information

Received: 10 December 2017; Revised: 27 May 2018; Accepted: 23 July 2018; Published: February, 2019
First available in Project Euclid: 1 August 2018

zbMATH: 07021725
MathSciNet: MR3909997
Digital Object Identifier: 10.11650/tjm/180705

Subjects:
Primary: 35A15, 35B33, 35J75

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.23 • No. 1 • February, 2019
Back to Top