Multiple solutions to elliptic equations on $\mathbb{R}^N$ with combined nonlinearities
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-10-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3558 |
| Summary: | 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. |
|---|---|
| ISSN: | 1417-3875 |