## Taiwanese Journal of Mathematics

### MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRÖDINGER-POISSON SYSTEMS WITH THE ASYMPTOTICAL NONLINEARITY IN $\mathbb{R}^3$

Ling Ding

#### Abstract

In this paper, we study nonhomogeneous Schrödinger-Poisson systems $\begin{cases} -\Delta u + u + K(x) \phi(x) u = a(x) f(u) + h(x), & x \in \mathbb{R}^3, \\ -\Delta \phi = K(x) u^2, & x \in \mathbb{R}^3, \end{cases}$ where $f(t)$ is either asymptotically linear or asymptotically 3-linear with respect to $t$ at infinity. Under appropriate assumptions on $K, a, f$ and $h$, the existence of two positive solutions of the above system is obtained by using the Ekeland's variational principle and the MountainPass Theorem in critical point theory.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 5 (2013), 1627-1650.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706229

Digital Object Identifier
doi:10.11650/tjm.17.2013.2798

Mathematical Reviews number (MathSciNet)
MR3106034

Zentralblatt MATH identifier
1281.35026

#### Citation

Ding, Ling. MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRÖDINGER-POISSON SYSTEMS WITH THE ASYMPTOTICAL NONLINEARITY IN $\mathbb{R}^3$. Taiwanese J. Math. 17 (2013), no. 5, 1627--1650. doi:10.11650/tjm.17.2013.2798. https://projecteuclid.org/euclid.twjm/1499706229

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