Topological Methods in Nonlinear Analysis

Infinitely many solutions to quasilinear elliptic equation with concave and convex terms

Leran Xia, Minbo Yang, and Fukun Zhao

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Abstract

In this paper, we are concerned with the following quasilinear elliptic equation with concave and convex terms \begin{equation} -\Delta u-{\frac12}\,u\Delta(|u|^2)=\alpha|u|^{p-2}u+\beta|u|^{q-2}u,\quad x\in \Omega, \tag($\rm P$) \end{equation} where $\Omega\subset\mathbb{R}^N$ is a bounded smooth domain, $1< p< 2$, $4< q\leq 22^*$. The existence of infinitely many solutions is obtained by the perturbation methods.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 2 (2014), 539-553.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381369

Mathematical Reviews number (MathSciNet)
MR3328355

Zentralblatt MATH identifier
1365.35042

Citation

Xia, Leran; Yang, Minbo; Zhao, Fukun. Infinitely many solutions to quasilinear elliptic equation with concave and convex terms. Topol. Methods Nonlinear Anal. 44 (2014), no. 2, 539--553. https://projecteuclid.org/euclid.tmna/1460381369


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