Multiple solutions to elliptic equations on $\mathbb{R}^N$ with combined nonlinearities

• Main Authors: Anran Li, Chongqing Wei
• Format: Article
• Language: English
• Published: University of Szeged 2015-10-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: weighted sobolev embedding; sublinear; asymptotically linear; superlinear; critical point theory; variation methods
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3558

In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equation \begin{equation*} \begin{cases} - \Delta u +V(x)u = -\lambda Q(x)|u|^{q-2}u+ Q(x)f(u),\quad x\in\mathbb{R}^N,\\ u(x)\rightarrow 0,\quad \hbox{as}\ |x|\rightarrow +\infty,\end{cases} \tag*{(P)$_\lambda$} \end{equation*} where $1<q<2,\ \lambda\in \mathbb{R}^+,\ N\geq 3$, $V$ and $Q$ are radial positive functions, which can be vanishing or coercive at infinity, $f$ is asymptotically linear or superlinear at infinity.