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.
Citation
Ling Ding. "MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRÖDINGER-POISSON SYSTEMS WITH THE ASYMPTOTICAL NONLINEARITY IN $\mathbb{R}^3$." Taiwanese J. Math. 17 (5) 1627 - 1650, 2013. https://doi.org/10.11650/tjm.17.2013.2798
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