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

Leran Xia, Minbo Yang, Fukun Zhao

Abstract


In this paper, we are concerned with the following quasilinear elliptic equation with concave and convex terms
$$
-\Delta u-{\frac12}u\Delta(|u|^2)=\alpha|u|^{p-2}u+\beta|u|^{q-2}u,\quad x\in
\Omega,
\leqno(\rom{P})
$$%
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.

Keywords


Concave and convex terms; fountain theorem; perturbation methods

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